Daily Papers

Stock prices forecasting has always been a challenging task. Although many research projects adopt machine learning and deep learning algorithms to address the problem, few of them pay attention to the varying degrees of dependencies between stock prices. In this paper we introduce a hybrid model that improves stock price prediction by emphasizing the dependencies between adjacent stock prices. The proposed model, ResNLS, is mainly composed of two neural architectures, ResNet and LSTM. ResNet serves as a feature extractor to identify dependencies between stock prices across time windows, while LSTM analyses the initial time-series data with the combination of dependencies which considered as residuals. In predicting the SSE Composite Index, our experiment reveals that when the closing price data for the previous 5 consecutive trading days is used as the input, the performance of the model (ResNLS-5) is optimal compared to those with other inputs. Furthermore, ResNLS-5 outperforms vanilla CNN, RNN, LSTM, and BiLSTM models in terms of prediction accuracy. It also demonstrates at least a 20% improvement over the current state-of-the-art baselines. To verify whether ResNLS-5 can help clients effectively avoid risks and earn profits in the stock market, we construct a quantitative trading framework for back testing. The experimental results show that the trading strategy based on predictions from ResNLS-5 can successfully mitigate losses during declining stock prices and generate profits in the periods of rising stock prices.

Designing robust frameworks for precise prediction of future prices of stocks has always been considered a very challenging research problem. The advocates of the classical efficient market hypothesis affirm that it is impossible to accurately predict the future prices in an efficiently operating market due to the stochastic nature of the stock price variables. However, numerous propositions exist in the literature with varying degrees of sophistication and complexity that illustrate how algorithms and models can be designed for making efficient, accurate, and robust predictions of stock prices. We present a gamut of ten deep learning models of regression for precise and robust prediction of the future prices of the stock of a critical company in the auto sector of India. Using a very granular stock price collected at 5 minutes intervals, we train the models based on the records from 31st Dec, 2012 to 27th Dec, 2013. The testing of the models is done using records from 30th Dec, 2013 to 9th Jan 2015. We explain the design principles of the models and analyze the results of their performance based on accuracy in forecasting and speed of execution.

There has been much interest in accurate cryptocurrency price forecast models by investors and researchers. Deep Learning models are prominent machine learning techniques that have transformed various fields and have shown potential for finance and economics. Although various deep learning models have been explored for cryptocurrency price forecasting, it is not clear which models are suitable due to high market volatility. In this study, we review the literature about deep learning for cryptocurrency price forecasting and evaluate novel deep learning models for cryptocurrency stock price prediction. Our deep learning models include variants of long short-term memory (LSTM) recurrent neural networks, variants of convolutional neural networks (CNNs), and the Transformer model. We evaluate univariate and multivariate approaches for multi-step ahead predicting of cryptocurrencies close-price. We also carry out volatility analysis on the four cryptocurrencies which reveals significant fluctuations in their prices throughout the COVID-19 pandemic. Additionally, we investigate the prediction accuracy of two scenarios identified by different training sets for the models. First, we use the pre-COVID-19 datasets to model cryptocurrency close-price forecasting during the early period of COVID-19. Secondly, we utilise data from the COVID-19 period to predict prices for 2023 to 2024. Our results show that the convolutional LSTM with a multivariate approach provides the best prediction accuracy in two major experimental settings. Our results also indicate that the multivariate deep learning models exhibit better performance in forecasting four different cryptocurrencies when compared to the univariate models.

We propose Adaptive Integrated Layered Attention (AILA), a neural network architecture that combines dense skip connections with different mechanisms for adaptive feature reuse across network layers. We evaluate AILA on three challenging tasks: price forecasting for various commodities and indices (S&P 500, Gold, US dollar Futures, Coffee, Wheat), image recognition using the CIFAR-10 dataset, and sentiment analysis on the IMDB movie review dataset. In all cases, AILA matches strong deep learning baselines (LSTMs, Transformers, and ResNets), achieving it at a fraction of the training and inference time. Notably, we implement and test two versions of the model - AILA-Architecture 1, which uses simple linear layers as the connection mechanism between layers, and AILA-Architecture 2, which implements an attention mechanism to selectively focus on outputs from previous layers. Both architectures are applied in a single-task learning setting, with each model trained separately for individual tasks. Results confirm that AILA's adaptive inter-layer connections yield robust gains by flexibly reusing pertinent features at multiple network depths. The AILA approach thus presents an extension to existing architectures, improving long-range sequence modeling, image recognition with optimised computational speed, and SOTA classification performance in practice.

Predicting stock market prices following corporate earnings calls remains a significant challenge for investors and researchers alike, requiring innovative approaches that can process diverse information sources. This study investigates the impact of corporate earnings calls on stock prices by introducing a multi-modal predictive model. We leverage textual data from earnings call transcripts, along with images and tables from accompanying presentations, to forecast stock price movements on the trading day immediately following these calls. To facilitate this research, we developed the MiMIC (Multi-Modal Indian Earnings Calls) dataset, encompassing companies representing the Nifty 50, Nifty MidCap 50, and Nifty Small 50 indices. The dataset includes earnings call transcripts, presentations, fundamentals, technical indicators, and subsequent stock prices. We present a multimodal analytical framework that integrates quantitative variables with predictive signals derived from textual and visual modalities, thereby enabling a holistic approach to feature representation and analysis. This multi-modal approach demonstrates the potential for integrating diverse information sources to enhance financial forecasting accuracy. To promote further research in computational economics, we have made the MiMIC dataset publicly available under the CC-NC-SA-4.0 licence. Our work contributes to the growing body of literature on market reactions to corporate communications and highlights the efficacy of multi-modal machine learning techniques in financial analysis.

The success of large-scale pre-training paradigm, exemplified by Large Language Models (LLMs), has inspired the development of Time Series Foundation Models (TSFMs). However, their application to financial candlestick (K-line) data remains limited, often underperforming non-pre-trained architectures. Moreover, existing TSFMs often overlook crucial downstream tasks such as volatility prediction and synthetic data generation. To address these limitations, we propose Kronos, a unified, scalable pre-training framework tailored to financial K-line modeling. Kronos introduces a specialized tokenizer that discretizes continuous market information into token sequences, preserving both price dynamics and trade activity patterns. We pre-train Kronos using an autoregressive objective on a massive, multi-market corpus of over 12 billion K-line records from 45 global exchanges, enabling it to learn nuanced temporal and cross-asset representations. Kronos excels in a zero-shot setting across a diverse set of financial tasks. On benchmark datasets, Kronos boosts price series forecasting RankIC by 93% over the leading TSFM and 87% over the best non-pre-trained baseline. It also achieves a 9% lower MAE in volatility forecasting and a 22% improvement in generative fidelity for synthetic K-line sequences. These results establish Kronos as a robust, versatile foundation model for end-to-end financial time series analysis. Our pre-trained model is publicly available at https://github.com/shiyu-coder/Kronos.

Weather forecasts are fundamentally uncertain, so predicting the range of probable weather scenarios is crucial for important decisions, from warning the public about hazardous weather, to planning renewable energy use. Here, we introduce GenCast, a probabilistic weather model with greater skill and speed than the top operational medium-range weather forecast in the world, the European Centre for Medium-Range Forecasts (ECMWF)'s ensemble forecast, ENS. Unlike traditional approaches, which are based on numerical weather prediction (NWP), GenCast is a machine learning weather prediction (MLWP) method, trained on decades of reanalysis data. GenCast generates an ensemble of stochastic 15-day global forecasts, at 12-hour steps and 0.25 degree latitude-longitude resolution, for over 80 surface and atmospheric variables, in 8 minutes. It has greater skill than ENS on 97.4% of 1320 targets we evaluated, and better predicts extreme weather, tropical cyclones, and wind power production. This work helps open the next chapter in operational weather forecasting, where critical weather-dependent decisions are made with greater accuracy and efficiency.

Machine learning (ML)-based weather models have rapidly risen to prominence due to their greater accuracy and speed than traditional forecasts based on numerical weather prediction (NWP), recently outperforming traditional ensembles in global probabilistic weather forecasting. This paper presents FGN, a simple, scalable and flexible modeling approach which significantly outperforms the current state-of-the-art models. FGN generates ensembles via learned model-perturbations with an ensemble of appropriately constrained models. It is trained directly to minimize the continuous rank probability score (CRPS) of per-location forecasts. It produces state-of-the-art ensemble forecasts as measured by a range of deterministic and probabilistic metrics, makes skillful ensemble tropical cyclone track predictions, and captures joint spatial structure despite being trained only on marginals.

Designing robust and accurate predictive models for stock price prediction has been an active area of research for a long time. While on one side, the supporters of the efficient market hypothesis claim that it is impossible to forecast stock prices accurately, many researchers believe otherwise. There exist propositions in the literature that have demonstrated that if properly designed and optimized, predictive models can very accurately and reliably predict future values of stock prices. This paper presents a suite of deep learning based models for stock price prediction. We use the historical records of the NIFTY 50 index listed in the National Stock Exchange of India, during the period from December 29, 2008 to July 31, 2020, for training and testing the models. Our proposition includes two regression models built on convolutional neural networks and three long and short term memory network based predictive models. To forecast the open values of the NIFTY 50 index records, we adopted a multi step prediction technique with walk forward validation. In this approach, the open values of the NIFTY 50 index are predicted on a time horizon of one week, and once a week is over, the actual index values are included in the training set before the model is trained again, and the forecasts for the next week are made. We present detailed results on the forecasting accuracies for all our proposed models. The results show that while all the models are very accurate in forecasting the NIFTY 50 open values, the univariate encoder decoder convolutional LSTM with the previous two weeks data as the input is the most accurate model. On the other hand, a univariate CNN model with previous one week data as the input is found to be the fastest model in terms of its execution speed.

Prediction of future movement of stock prices has been a subject matter of many research work. In this work, we propose a hybrid approach for stock price prediction using machine learning and deep learning-based methods. We select the NIFTY 50 index values of the National Stock Exchange of India, over a period of four years, from January 2015 till December 2019. Based on the NIFTY data during the said period, we build various predictive models using machine learning approaches, and then use those models to predict the Close value of NIFTY 50 for the year 2019, with a forecast horizon of one week. For predicting the NIFTY index movement patterns, we use a number of classification methods, while for forecasting the actual Close values of NIFTY index, various regression models are built. We, then, augment our predictive power of the models by building a deep learning-based regression model using Convolutional Neural Network with a walk-forward validation. The CNN model is fine-tuned for its parameters so that the validation loss stabilizes with increasing number of iterations, and the training and validation accuracies converge. We exploit the power of CNN in forecasting the future NIFTY index values using three approaches which differ in number of variables used in forecasting, number of sub-models used in the overall models and, size of the input data for training the models. Extensive results are presented on various metrics for all classification and regression models. The results clearly indicate that CNN-based multivariate forecasting model is the most effective and accurate in predicting the movement of NIFTY index values with a weekly forecast horizon.

Prediction of stock price and stock price movement patterns has always been a critical area of research. While the well-known efficient market hypothesis rules out any possibility of accurate prediction of stock prices, there are formal propositions in the literature demonstrating accurate modeling of the predictive systems that can enable us to predict stock prices with a very high level of accuracy. In this paper, we present a suite of deep learning-based regression models that yields a very high level of accuracy in stock price prediction. To build our predictive models, we use the historical stock price data of a well-known company listed in the National Stock Exchange (NSE) of India during the period December 31, 2012 to January 9, 2015. The stock prices are recorded at five minutes intervals of time during each working day in a week. Using these extremely granular stock price data, we build four convolutional neural network (CNN) and five long- and short-term memory (LSTM)-based deep learning models for accurate forecasting of the future stock prices. We provide detailed results on the forecasting accuracies of all our proposed models based on their execution time and their root mean square error (RMSE) values.

Prediction of stock prices has been an important area of research for a long time. While supporters of the efficient market hypothesis believe that it is impossible to predict stock prices accurately, there are formal propositions demonstrating that accurate modeling and designing of appropriate variables may lead to models using which stock prices and stock price movement patterns can be very accurately predicted. In this work, we propose an approach of hybrid modeling for stock price prediction building different machine learning and deep learning-based models. For the purpose of our study, we have used NIFTY 50 index values of the National Stock Exchange (NSE) of India, during the period December 29, 2014 till July 31, 2020. We have built eight regression models using the training data that consisted of NIFTY 50 index records during December 29, 2014 till December 28, 2018. Using these regression models, we predicted the open values of NIFTY 50 for the period December 31, 2018 till July 31, 2020. We, then, augment the predictive power of our forecasting framework by building four deep learning-based regression models using long-and short-term memory (LSTM) networks with a novel approach of walk-forward validation. We exploit the power of LSTM regression models in forecasting the future NIFTY 50 open values using four different models that differ in their architecture and in the structure of their input data. Extensive results are presented on various metrics for the all the regression models. The results clearly indicate that the LSTM-based univariate model that uses one-week prior data as input for predicting the next week open value of the NIFTY 50 time series is the most accurate model.

Armed conflict has led to an unprecedented number of internally displaced persons (IDPs) - individuals who are forced out of their homes but remain within their country. IDPs often urgently require shelter, food, and healthcare, yet prediction of when large fluxes of IDPs will cross into an area remains a major challenge for aid delivery organizations. Accurate forecasting of IDP migration would empower humanitarian aid groups to more effectively allocate resources during conflicts. We show that monthly flow of IDPs from province to province in both Syria and Yemen can be accurately forecasted one month in advance, using publicly available data. We model monthly IDP flow using data on food price, fuel price, wage, geospatial, and news data. We find that machine learning approaches can more accurately forecast migration trends than baseline persistence models. Our findings thus potentially enable proactive aid allocation for IDPs in anticipation of forecasted arrivals.

Prediction of stock prices plays a significant role in aiding the decision-making of investors. Considering its importance, a growing literature has emerged trying to forecast stock prices with improved accuracy. In this study, we introduce an innovative approach for forecasting stock prices with greater accuracy. We incorporate external economic environment-related information along with stock prices. In our novel approach, we improve the performance of stock price prediction by taking into account variations due to future expected macroeconomic policy changes as investors adjust their current behavior ahead of time based on expected future macroeconomic policy changes. Furthermore, we incorporate macroeconomic variables along with historical stock prices to make predictions. Results from this strongly support the inclusion of future economic policy changes along with current macroeconomic information. We confirm the supremacy of our method over the conventional approach using several tree-based machine-learning algorithms. Results are strongly conclusive across various machine learning models. Our preferred model outperforms the conventional approach with an RMSE value of 1.61 compared to an RMSE value of 1.75 from the conventional approach.

For a long-time, researchers have been developing a reliable and accurate predictive model for stock price prediction. According to the literature, if predictive models are correctly designed and refined, they can painstakingly and faithfully estimate future stock values. This paper demonstrates a set of time series, econometric, and various learning-based models for stock price prediction. The data of Infosys, ICICI, and SUN PHARMA from the period of January 2004 to December 2019 was used here for training and testing the models to know which model performs best in which sector. One time series model (Holt-Winters Exponential Smoothing), one econometric model (ARIMA), two machine Learning models (Random Forest and MARS), and two deep learning-based models (simple RNN and LSTM) have been included in this paper. MARS has been proved to be the best performing machine learning model, while LSTM has proved to be the best performing deep learning model. But overall, for all three sectors - IT (on Infosys data), Banking (on ICICI data), and Health (on SUN PHARMA data), MARS has proved to be the best performing model in sales forecasting.

Time series forecasting is important across various domains for decision-making. In particular, financial time series such as stock prices can be hard to predict as it is difficult to model short-term and long-term temporal dependencies between data points. Convolutional Neural Networks (CNN) are good at capturing local patterns for modeling short-term dependencies. However, CNNs cannot learn long-term dependencies due to the limited receptive field. Transformers on the other hand are capable of learning global context and long-term dependencies. In this paper, we propose to harness the power of CNNs and Transformers to model both short-term and long-term dependencies within a time series, and forecast if the price would go up, down or remain the same (flat) in the future. In our experiments, we demonstrated the success of the proposed method in comparison to commonly adopted statistical and deep learning methods on forecasting intraday stock price change of S&P 500 constituents.

Using a large-scale Deep Learning approach applied to a high-frequency database containing billions of electronic market quotes and transactions for US equities, we uncover nonparametric evidence for the existence of a universal and stationary price formation mechanism relating the dynamics of supply and demand for a stock, as revealed through the order book, to subsequent variations in its market price. We assess the model by testing its out-of-sample predictions for the direction of price moves given the history of price and order flow, across a wide range of stocks and time periods. The universal price formation model is shown to exhibit a remarkably stable out-of-sample prediction accuracy across time, for a wide range of stocks from different sectors. Interestingly, these results also hold for stocks which are not part of the training sample, showing that the relations captured by the model are universal and not asset-specific. The universal model --- trained on data from all stocks --- outperforms, in terms of out-of-sample prediction accuracy, asset-specific linear and nonlinear models trained on time series of any given stock, showing that the universal nature of price formation weighs in favour of pooling together financial data from various stocks, rather than designing asset- or sector-specific models as commonly done. Standard data normalizations based on volatility, price level or average spread, or partitioning the training data into sectors or categories such as large/small tick stocks, do not improve training results. On the other hand, inclusion of price and order flow history over many past observations is shown to improve forecasting performance, showing evidence of path-dependence in price dynamics.

In this paper, we develop a hybrid approach to forecasting the volatility and risk of financial instruments by combining common econometric GARCH time series models with deep learning neural networks. For the latter, we employ Gated Recurrent Unit (GRU) networks, whereas four different specifications are used as the GARCH component: standard GARCH, EGARCH, GJR-GARCH and APARCH. Models are tested using daily logarithmic returns on the S&P 500 index as well as gold price Bitcoin prices, with the three assets representing quite distinct volatility dynamics. As the main volatility estimator, also underlying the target function of our hybrid models, we use the price-range-based Garman-Klass estimator, modified to incorporate the opening and closing prices. Volatility forecasts resulting from the hybrid models are employed to evaluate the assets' risk using the Value-at-Risk (VaR) and Expected Shortfall (ES) at two different tolerance levels of 5% and 1%. Gains from combining the GARCH and GRU approaches are discussed in the contexts of both the volatility and risk forecasts. In general, it can be concluded that the hybrid solutions produce more accurate point volatility forecasts, although it does not necessarily translate into superior VaR and ES forecasts.

Prediction of future movement of stock prices has always been a challenging task for the researchers. While the advocates of the efficient market hypothesis (EMH) believe that it is impossible to design any predictive framework that can accurately predict the movement of stock prices, there are seminal work in the literature that have clearly demonstrated that the seemingly random movement patterns in the time series of a stock price can be predicted with a high level of accuracy. Design of such predictive models requires choice of appropriate variables, right transformation methods of the variables, and tuning of the parameters of the models. In this work, we present a very robust and accurate framework of stock price prediction that consists of an agglomeration of statistical, machine learning and deep learning models. We use the daily stock price data, collected at five minutes interval of time, of a very well known company that is listed in the National Stock Exchange (NSE) of India. The granular data is aggregated into three slots in a day, and the aggregated data is used for building and training the forecasting models. We contend that the agglomerative approach of model building that uses a combination of statistical, machine learning, and deep learning approaches, can very effectively learn from the volatile and random movement patterns in a stock price data. We build eight classification and eight regression models based on statistical and machine learning approaches. In addition to these models, a deep learning regression model using a long-and-short-term memory (LSTM) network is also built. Extensive results have been presented on the performance of these models, and the results are critically analyzed.

We introduce Ego4D, a massive-scale egocentric video dataset and benchmark suite. It offers 3,670 hours of daily-life activity video spanning hundreds of scenarios (household, outdoor, workplace, leisure, etc.) captured by 931 unique camera wearers from 74 worldwide locations and 9 different countries. The approach to collection is designed to uphold rigorous privacy and ethics standards with consenting participants and robust de-identification procedures where relevant. Ego4D dramatically expands the volume of diverse egocentric video footage publicly available to the research community. Portions of the video are accompanied by audio, 3D meshes of the environment, eye gaze, stereo, and/or synchronized videos from multiple egocentric cameras at the same event. Furthermore, we present a host of new benchmark challenges centered around understanding the first-person visual experience in the past (querying an episodic memory), present (analyzing hand-object manipulation, audio-visual conversation, and social interactions), and future (forecasting activities). By publicly sharing this massive annotated dataset and benchmark suite, we aim to push the frontier of first-person perception. Project page: https://ego4d-data.org/

This paper presents a comprehensive study on stock price prediction, leveragingadvanced machine learning (ML) and deep learning (DL) techniques to improve financial forecasting accuracy. The research evaluates the performance of various recurrent neural network (RNN) architectures, including Long Short-Term Memory (LSTM) networks, Gated Recurrent Units (GRU), and attention-based models. These models are assessed for their ability to capture complex temporal dependencies inherent in stock market data. Our findings show that attention-based models outperform other architectures, achieving the highest accuracy by capturing both short and long-term dependencies. This study contributes valuable insights into AI-driven financial forecasting, offering practical guidance for developing more accurate and efficient trading systems.

As global fertilizer application rates increase, high-quality datasets are paramount for comprehensive analyses to support informed decision-making and policy formulation in crucial areas such as food security or climate change. This study aims to fill existing data gaps by employing two machine learning models, eXtreme Gradient Boosting and HistGradientBoosting algorithms to produce precise country-level predictions of nitrogen (N), phosphorus pentoxide (P_2O_5), and potassium oxide (K_2O) application rates. Subsequently, we created a comprehensive dataset of 5-arcmin resolution maps depicting the application rates of each fertilizer for 13 major crop groups from 1961 to 2019. The predictions were validated by both comparing with existing databases and by assessing the drivers of fertilizer application rates using the model's SHapley Additive exPlanations. This extensive dataset is poised to be a valuable resource for assessing fertilization trends, identifying the socioeconomic, agricultural, and environmental drivers of fertilizer application rates, and serving as an input for various applications, including environmental modeling, causal analysis, fertilizer price predictions, and forecasting.

Predictive model design for accurately predicting future stock prices has always been considered an interesting and challenging research problem. The task becomes complex due to the volatile and stochastic nature of the stock prices in the real world which is affected by numerous controllable and uncontrollable variables. This paper presents an optimized predictive model built on long-and-short-term memory (LSTM) architecture for automatically extracting past stock prices from the web over a specified time interval and predicting their future prices for a specified forecast horizon, and forecasts the future stock prices. The model is deployed for making buy and sell transactions based on its predicted results for 70 important stocks from seven different sectors listed in the National Stock Exchange (NSE) of India. The profitability of each sector is derived based on the total profit yielded by the stocks in that sector over a period from Jan 1, 2010 to Aug 26, 2021. The sectors are compared based on their profitability values. The prediction accuracy of the model is also evaluated for each sector. The results indicate that the model is highly accurate in predicting future stock prices.

Designing robust systems for precise prediction of future prices of stocks has always been considered a very challenging research problem. Even more challenging is to build a system for constructing an optimum portfolio of stocks based on the forecasted future stock prices. We present a deep learning-based regression model built on a long-and-short-term memory network (LSTM) network that automatically scraps the web and extracts historical stock prices based on a stock's ticker name for a specified pair of start and end dates, and forecasts the future stock prices. We deploy the model on 75 significant stocks chosen from 15 critical sectors of the Indian stock market. For each of the stocks, the model is evaluated for its forecast accuracy. Moreover, the predicted values of the stock prices are used as the basis for investment decisions, and the returns on the investments are computed. Extensive results are presented on the performance of the model. The analysis of the results demonstrates the efficacy and effectiveness of the system and enables us to compare the profitability of the sectors from the point of view of the investors in the stock market.

Recognizing that traditional forecasting models often rely solely on historical demand, this work investigates the potential of data-driven techniques to automatically select and integrate market indicators for improving customer demand predictions. By adopting an exploratory methodology, we integrate macroeconomic time series, such as national GDP growth, from the Eurostat database into Neural Prophet and SARIMAX forecasting models. Suitable time series are automatically identified through different state-of-the-art feature selection methods and applied to sales data from our industrial partner. It could be shown that forecasts can be significantly enhanced by incorporating external information. Notably, the potential of feature selection methods stands out, especially due to their capability for automation without expert knowledge and manual selection effort. In particular, the Forward Feature Selection technique consistently yielded superior forecasting accuracy for both SARIMAX and Neural Prophet across different company sales datasets. In the comparative analysis of the errors of the selected forecasting models, namely Neural Prophet and SARIMAX, it is observed that neither model demonstrates a significant superiority over the other.

Traditional time-series forecasting often focuses only on minimizing prediction errors, ignoring the specific requirements of real-world applications that employ them. This paper presents a new training methodology, which allows a forecasting model to dynamically adjust its focus based on the importance of forecast ranges specified by the end application. Unlike previous methods that fix these ranges beforehand, our training approach breaks down predictions over the entire signal range into smaller segments, which are then dynamically weighted and combined to produce accurate forecasts. We tested our method on standard datasets, including a new dataset from wireless communication, and found that not only it improves prediction accuracy but also improves the performance of end application employing the forecasting model. This research provides a basis for creating forecasting systems that better connect prediction and decision-making in various practical applications.

International trade policies have recently garnered attention for limiting cross-border exchange of essential goods (e.g. steel, aluminum, soybeans, and beef). Since trade critically affects employment and wages, predicting future patterns of trade is a high-priority for policy makers around the world. While traditional economic models aim to be reliable predictors, we consider the possibility that Machine Learning (ML) techniques allow for better predictions to inform policy decisions. Open-government data provide the fuel to power the algorithms that can explain and forecast trade flows to inform policies. Data collected in this article describe international trade transactions and commonly associated economic factors. Machine learning (ML) models deployed include: ARIMA, GBoosting, XGBoosting, and LightGBM for predicting future trade patterns, and K-Means clustering of countries according to economic factors. Unlike short-term and subjective (straight-line) projections and medium-term (aggre-gated) projections, ML methods provide a range of data-driven and interpretable projections for individual commodities. Models, their results, and policies are introduced and evaluated for prediction quality.

Forecasting is a critical task in decision-making across numerous domains. While historical numerical data provide a start, they fail to convey the complete context for reliable and accurate predictions. Human forecasters frequently rely on additional information, such as background knowledge and constraints, which can efficiently be communicated through natural language. However, in spite of recent progress with LLM-based forecasters, their ability to effectively integrate this textual information remains an open question. To address this, we introduce "Context is Key" (CiK), a time-series forecasting benchmark that pairs numerical data with diverse types of carefully crafted textual context, requiring models to integrate both modalities; crucially, every task in CiK requires understanding textual context to be solved successfully. We evaluate a range of approaches, including statistical models, time series foundation models, and LLM-based forecasters, and propose a simple yet effective LLM prompting method that outperforms all other tested methods on our benchmark. Our experiments highlight the importance of incorporating contextual information, demonstrate surprising performance when using LLM-based forecasting models, and also reveal some of their critical shortcomings. This benchmark aims to advance multimodal forecasting by promoting models that are both accurate and accessible to decision-makers with varied technical expertise. The benchmark can be visualized at https://servicenow.github.io/context-is-key-forecasting/v0/.

Forecasting is an important task in many domains, such as technology and economics. However existing forecasting benchmarks largely lack comprehensive confidence assessment, focus on limited question types, and often consist of artificial questions that do not align with real-world human forecasting needs. To address these gaps, we introduce FOReCAst (Future Outcome Reasoning and Confidence Assessment), a benchmark that evaluates models' ability to make predictions and their confidence in them. FOReCAst spans diverse forecasting scenarios involving Boolean questions, timeframe prediction, and quantity estimation, enabling a comprehensive evaluation of both prediction accuracy and confidence calibration for real-world applications.

Predicting future stock prices and their movement patterns is a complex problem. Hence, building a portfolio of capital assets using the predicted prices to achieve the optimization between its return and risk is an even more difficult task. This work has carried out an analysis of the time series of the historical prices of the top five stocks from the nine different sectors of the Indian stock market from January 1, 2016, to December 31, 2020. Optimum portfolios are built for each of these sectors. For predicting future stock prices, a long-and-short-term memory (LSTM) model is also designed and fine-tuned. After five months of the portfolio construction, the actual and the predicted returns and risks of each portfolio are computed. The predicted and the actual returns of each portfolio are found to be high, indicating the high precision of the LSTM model.

Building predictive models for robust and accurate prediction of stock prices and stock price movement is a challenging research problem to solve. The well-known efficient market hypothesis believes in the impossibility of accurate prediction of future stock prices in an efficient stock market as the stock prices are assumed to be purely stochastic. However, numerous works proposed by researchers have demonstrated that it is possible to predict future stock prices with a high level of precision using sophisticated algorithms, model architectures, and the selection of appropriate variables in the models. This chapter proposes a collection of predictive regression models built on deep learning architecture for robust and precise prediction of the future prices of a stock listed in the diversified sectors in the National Stock Exchange (NSE) of India. The Metastock tool is used to download the historical stock prices over a period of two years (2013- 2014) at 5 minutes intervals. While the records for the first year are used to train the models, the testing is carried out using the remaining records. The design approaches of all the models and their performance results are presented in detail. The models are also compared based on their execution time and accuracy of prediction.

The prediction of foreign exchange rates, such as the US Dollar (USD) to Bangladeshi Taka (BDT), plays a pivotal role in global financial markets, influencing trade, investments, and economic stability. This study leverages historical USD/BDT exchange rate data from 2018 to 2023, sourced from Yahoo Finance, to develop advanced machine learning models for accurate forecasting. A Long Short-Term Memory (LSTM) neural network is employed, achieving an exceptional accuracy of 99.449%, a Root Mean Square Error (RMSE) of 0.9858, and a test loss of 0.8523, significantly outperforming traditional methods like ARIMA (RMSE 1.342). Additionally, a Gradient Boosting Classifier (GBC) is applied for directional prediction, with backtesting on a 10,000 initial capital revealing a 40.82% profitable trade rate, though resulting in a net loss of 20,653.25 over 49 trades. The study analyzes historical trends, showing a decline in BDT/USD rates from 0.012 to 0.009, and incorporates normalized daily returns to capture volatility. These findings highlight the potential of deep learning in forex forecasting, offering traders and policymakers robust tools to mitigate risks. Future work could integrate sentiment analysis and real-time economic indicators to further enhance model adaptability in volatile markets.

Forecasting future events is important for policy and decision making. In this work, we study whether language models (LMs) can forecast at the level of competitive human forecasters. Towards this goal, we develop a retrieval-augmented LM system designed to automatically search for relevant information, generate forecasts, and aggregate predictions. To facilitate our study, we collect a large dataset of questions from competitive forecasting platforms. Under a test set published after the knowledge cut-offs of our LMs, we evaluate the end-to-end performance of our system against the aggregates of human forecasts. On average, the system nears the crowd aggregate of competitive forecasters, and in some settings surpasses it. Our work suggests that using LMs to forecast the future could provide accurate predictions at scale and help to inform institutional decision making.

One of the challenging research problems in the domain of time series analysis and forecasting is making efficient and robust prediction of stock market prices. With rapid development and evolution of sophisticated algorithms and with the availability of extremely fast computing platforms, it has now become possible to effectively extract, store, process and analyze high volume stock market time series data. Complex algorithms for forecasting are now available for speedy execution over parallel architecture leading to fairly accurate results. In this paper, we have used time series data of the two sectors of the Indian economy: Consumer Durables sector and the Small Cap sector for the period January 2010 to December 2015 and proposed a decomposition approach for better understanding of the behavior of each of the time series. Our contention is that various sectors reveal different time series patterns and understanding them is essential for portfolio formation. Further, based on this structural analysis, we have also proposed several robust forecasting techniques and analyzed their accuracy in prediction using suitably chosen training and test data sets. Extensive results are presented to demonstrate the effectiveness of our propositions.

Foundation Models (FMs) have improved time series forecasting in various sectors, such as finance, but their vulnerability to input disturbances can hinder their adoption by stakeholders, such as investors and analysts. To address this, we propose a causally grounded rating framework to study the robustness of Foundational Models for Time Series (FMTS) with respect to input perturbations. We evaluate our approach to the stock price prediction problem, a well-studied problem with easily accessible public data, evaluating six state-of-the-art (some multi-modal) FMTS across six prominent stocks spanning three industries. The ratings proposed by our framework effectively assess the robustness of FMTS and also offer actionable insights for model selection and deployment. Within the scope of our study, we find that (1) multi-modal FMTS exhibit better robustness and accuracy compared to their uni-modal versions and, (2) FMTS pre-trained on time series forecasting task exhibit better robustness and forecasting accuracy compared to general-purpose FMTS pre-trained across diverse settings. Further, to validate our framework's usability, we conduct a user study showcasing FMTS prediction errors along with our computed ratings. The study confirmed that our ratings reduced the difficulty for users in comparing the robustness of different systems.

Forecasts of future events are essential inputs into informed decision-making. Machine learning (ML) systems have the potential to deliver forecasts at scale, but there is no framework for evaluating the accuracy of ML systems on a standardized set of forecasting questions. To address this gap, we introduce ForecastBench: a dynamic benchmark that evaluates the accuracy of ML systems on an automatically generated and regularly updated set of 1,000 forecasting questions. To avoid any possibility of data leakage, ForecastBench is comprised solely of questions about future events that have no known answer at the time of submission. We quantify the capabilities of current ML systems by collecting forecasts from expert (human) forecasters, the general public, and LLMs on a random subset of questions from the benchmark (N=200). While LLMs have achieved super-human performance on many benchmarks, they perform less well here: expert forecasters outperform the top-performing LLM (p-value <0.001). We display system and human scores in a public leaderboard at www.forecastbench.org.

Accurate prediction of future prices of stocks is a difficult task to perform. Even more challenging is to design an optimized portfolio of stocks with the identification of proper weights of allocation to achieve the optimized values of return and risk. We present optimized portfolios based on the seven sectors of the Indian economy. The past prices of the stocks are extracted from the web from January 1, 2016, to December 31, 2020. Optimum portfolios are designed on the selected seven sectors. An LSTM regression model is also designed for predicting future stock prices. Five months after the construction of the portfolios, i.e., on June 1, 2021, the actual and predicted returns and risks of each portfolio are computed. The predicted and the actual returns indicate the very high accuracy of the LSTM model.

The fundamental theorem behind financial markets is that stock prices are intrinsically complex and stochastic. One of the complexities is the volatility associated with stock prices. Volatility is a tendency for prices to change unexpectedly [1]. Price volatility is often detrimental to the return economics, and thus, investors should factor it in whenever making investment decisions, choices, and temporal or permanent moves. It is, therefore, crucial to make necessary and regular short and long-term stock price volatility forecasts for the safety and economics of investors returns. These forecasts should be accurate and not misleading. Different models and methods, such as ARCH GARCH models, have been intuitively implemented to make such forecasts. However, such traditional means fail to capture the short-term volatility forecasts effectively. This paper, therefore, investigates and implements a combination of numeric and probabilistic models for short-term volatility and return forecasting for high-frequency trades. The essence is that one-day-ahead volatility forecasts were made with Gaussian Processes (GPs) applied to the outputs of a Numerical market prediction (NMP) model. Firstly, the stock price data from NMP was corrected by a GP. Since it is not easy to set price limits in a market due to its free nature and randomness, a Censored GP was used to model the relationship between the corrected stock prices and returns. Forecasting errors were evaluated using the implied and estimated data.

Stock prediction is a topic undergoing intense study for many years. Finance experts and mathematicians have been working on a way to predict the future stock price so as to decide to buy the stock or sell it to make profit. Stock experts or economists, usually analyze on the previous stock values using technical indicators, sentiment analysis etc to predict the future stock price. In recent years, many researches have extensively used machine learning for predicting the stock behaviour. In this paper we propose data driven deep learning approach to predict the future stock value with the previous price with the feature extraction property of convolutional neural network and to use Neural Arithmetic Logic Units with it.

Analyzing both temporal and spatial patterns for an accurate forecasting model for financial time series forecasting is a challenge due to the complex nature of temporal-spatial dynamics: time series from different locations often have distinct patterns; and for the same time series, patterns may vary as time goes by. Inspired by the successful applications of deep learning, we propose a new model to resolve the issues of forecasting household leverage in China. Our solution consists of multiple RNN-based layers and an attention layer: each RNN-based layer automatically learns the temporal pattern of a specific series with multivariate exogenous series, and then the attention layer learns the spatial correlative weight and obtains the global representations simultaneously. The results show that the new approach can capture the temporal-spatial dynamics of household leverage well and get more accurate and solid predictive results. More, the simulation also studies show that clustering and choosing correlative series are necessary to obtain accurate forecasting results.

AI systems are notorious for their fragility; minor input changes can potentially cause major output swings. When such systems are deployed in critical areas like finance, the consequences of their uncertain behavior could be severe. In this paper, we focus on multi-modal time-series forecasting, where imprecision due to noisy or incorrect data can lead to erroneous predictions, impacting stakeholders such as analysts, investors, and traders. Recently, it has been shown that beyond numeric data, graphical transformations can be used with advanced visual models to achieve better performance. In this context, we introduce a rating methodology to assess the robustness of Multi-Modal Time-Series Forecasting Models (MM-TSFM) through causal analysis, which helps us understand and quantify the isolated impact of various attributes on the forecasting accuracy of MM-TSFM. We apply our novel rating method on a variety of numeric and multi-modal forecasting models in a large experimental setup (six input settings of control and perturbations, ten data distributions, time series from six leading stocks in three industries over a year of data, and five time-series forecasters) to draw insights on robust forecasting models and the context of their strengths. Within the scope of our study, our main result is that multi-modal (numeric + visual) forecasting, which was found to be more accurate than numeric forecasting in previous studies, can also be more robust in diverse settings. Our work will help different stakeholders of time-series forecasting understand the models` behaviors along trust (robustness) and accuracy dimensions to select an appropriate model for forecasting using our rating method, leading to improved decision-making.

Many businesses and industries nowadays rely on large quantities of time series data making time series forecasting an important research area. Global forecasting models that are trained across sets of time series have shown a huge potential in providing accurate forecasts compared with the traditional univariate forecasting models that work on isolated series. However, there are currently no comprehensive time series archives for forecasting that contain datasets of time series from similar sources available for the research community to evaluate the performance of new global forecasting algorithms over a wide variety of datasets. In this paper, we present such a comprehensive time series forecasting archive containing 20 publicly available time series datasets from varied domains, with different characteristics in terms of frequency, series lengths, and inclusion of missing values. We also characterise the datasets, and identify similarities and differences among them, by conducting a feature analysis. Furthermore, we present the performance of a set of standard baseline forecasting methods over all datasets across eight error metrics, for the benefit of researchers using the archive to benchmark their forecasting algorithms.

Pure time series forecasting tasks typically focus exclusively on numerical features; however, real-world financial decision-making demands the comparison and analysis of heterogeneous sources of information. Recent advances in deep learning and large scale language models (LLMs) have made significant strides in capturing sentiment and other qualitative signals, thereby enhancing the accuracy of financial time series predictions. Despite these advances, most existing datasets consist solely of price series and news text, are confined to a single market, and remain limited in scale. In this paper, we introduce FinMultiTime, the first large scale, multimodal financial time series dataset. FinMultiTime temporally aligns four distinct modalities financial news, structured financial tables, K-line technical charts, and stock price time series across both the S&P 500 and HS 300 universes. Covering 5,105 stocks from 2009 to 2025 in the United States and China, the dataset totals 112.6 GB and provides minute-level, daily, and quarterly resolutions, thus capturing short, medium, and long term market signals with high fidelity. Our experiments demonstrate that (1) scale and data quality markedly boost prediction accuracy; (2) multimodal fusion yields moderate gains in Transformer models; and (3) a fully reproducible pipeline enables seamless dataset updates.

We introduce NeuralProphet, a successor to Facebook Prophet, which set an industry standard for explainable, scalable, and user-friendly forecasting frameworks. With the proliferation of time series data, explainable forecasting remains a challenging task for business and operational decision making. Hybrid solutions are needed to bridge the gap between interpretable classical methods and scalable deep learning models. We view Prophet as a precursor to such a solution. However, Prophet lacks local context, which is essential for forecasting the near-term future and is challenging to extend due to its Stan backend. NeuralProphet is a hybrid forecasting framework based on PyTorch and trained with standard deep learning methods, making it easy for developers to extend the framework. Local context is introduced with auto-regression and covariate modules, which can be configured as classical linear regression or as Neural Networks. Otherwise, NeuralProphet retains the design philosophy of Prophet and provides the same basic model components. Our results demonstrate that NeuralProphet produces interpretable forecast components of equivalent or superior quality to Prophet on a set of generated time series. NeuralProphet outperforms Prophet on a diverse collection of real-world datasets. For short to medium-term forecasts, NeuralProphet improves forecast accuracy by 55 to 92 percent.

Accurate prediction of future prices of stocks is a difficult task to perform. Even more challenging is to design an optimized portfolio with weights allocated to the stocks in a way that optimizes its return and the risk. This paper presents a systematic approach towards building two types of portfolios, optimum risk, and eigen, for four critical economic sectors of India. The prices of the stocks are extracted from the web from Jan 1, 2016, to Dec 31, 2020. Sector-wise portfolios are built based on their ten most significant stocks. An LSTM model is also designed for predicting future stock prices. Six months after the construction of the portfolios, i.e., on Jul 1, 2021, the actual returns and the LSTM-predicted returns for the portfolios are computed. A comparison of the predicted and the actual returns indicate a high accuracy level of the LSTM model.

Designing efficient and robust algorithms for accurate prediction of stock market prices is one of the most exciting challenges in the field of time series analysis and forecasting. With the exponential rate of development and evolution of sophisticated algorithms and with the availability of fast computing platforms, it has now become possible to effectively and efficiently extract, store, process and analyze high volume of stock market data with diversity in its contents. Availability of complex algorithms which can execute very fast on parallel architecture over the cloud has made it possible to achieve higher accuracy in forecasting results while reducing the time required for computation. In this paper, we use the time series data of the healthcare sector of India for the period January 2010 till December 2016. We first demonstrate a decomposition approach of the time series and then illustrate how the decomposition results provide us with useful insights into the behavior and properties exhibited by the time series. Further, based on the structural analysis of the time series, we propose six different methods of forecasting for predicting the time series index of the healthcare sector. Extensive results are provided on the performance of the forecasting methods to demonstrate their effectiveness.

Stock selection, which aims to predict stock prices and identify the most profitable ones, is a crucial task in finance. While existing methods primarily focus on developing model structures and building graphs for improved selection, pre-training strategies remain underexplored in this domain. Current stock series pre-training follows methods from other areas without adapting to the unique characteristics of financial data, particularly overlooking stock-specific contextual information and the non-stationary nature of stock prices. Consequently, the latent statistical features inherent in stock data are underutilized. In this paper, we propose three novel pre-training tasks tailored to stock data characteristics: stock code classification, stock sector classification, and moving average prediction. We develop the Stock Specialized Pre-trained Transformer (SSPT) based on a two-layer transformer architecture. Extensive experimental results validate the effectiveness of our pre-training methods and provide detailed guidance on their application. Evaluations on five stock datasets, including four markets and two time periods, demonstrate that SSPT consistently outperforms the market and existing methods in terms of both cumulative investment return ratio and Sharpe ratio. Additionally, our experiments on simulated data investigate the underlying mechanisms of our methods, providing insights into understanding price series. Our code is publicly available at: https://github.com/astudentuser/Pre-training-Time-Series-Models-with-Stock-Data-Customization.

Prediction of future movement of stock prices has been a subject matter of many research work. There is a gamut of literature of technical analysis of stock prices where the objective is to identify patterns in stock price movements and derive profit from it. Improving the prediction accuracy remains the single most challenge in this area of research. We propose a hybrid approach for stock price movement prediction using machine learning, deep learning, and natural language processing. We select the NIFTY 50 index values of the National Stock Exchange of India, and collect its daily price movement over a period of three years (2015 to 2017). Based on the data of 2015 to 2017, we build various predictive models using machine learning, and then use those models to predict the closing value of NIFTY 50 for the period January 2018 till June 2019 with a prediction horizon of one week. For predicting the price movement patterns, we use a number of classification techniques, while for predicting the actual closing price of the stock, various regression models have been used. We also build a Long and Short-Term Memory - based deep learning network for predicting the closing price of the stocks and compare the prediction accuracies of the machine learning models with the LSTM model. We further augment the predictive model by integrating a sentiment analysis module on twitter data to correlate the public sentiment of stock prices with the market sentiment. This has been done using twitter sentiment and previous week closing values to predict stock price movement for the next week. We tested our proposed scheme using a cross validation method based on Self Organizing Fuzzy Neural Networks and found extremely interesting results.

Financial markets have a vital role in the development of modern society. They allow the deployment of economic resources. Changes in stock prices reflect changes in the market. In this study, we focus on predicting stock prices by deep learning model. This is a challenge task, because there is much noise and uncertainty in information that is related to stock prices. So this work uses sparse autoencoders with one-dimension (1-D) residual convolutional networks which is a deep learning model, to de-noise the data. Long-short term memory (LSTM) is then used to predict the stock price. The prices, indices and macroeconomic variables in past are the features used to predict the next day's price. Experiment results show that 1-D residual convolutional networks can de-noise data and extract deep features better than a model that combines wavelet transforms (WT) and stacked autoencoders (SAEs). In addition, we compare the performances of model with two different forecast targets of stock price: absolute stock price and price rate of change. The results show that predicting stock price through price rate of change is better than predicting absolute prices directly.

Machine learning for time-series forecasting remains a key area of research. Despite successful application of many machine learning techniques, relating computational efficiency to forecast error remains an under-explored domain. This paper addresses this topic through a series of real-time experiments to quantify the relationship between computational cost and forecast error using meteorological nowcasting as an example use-case. We employ a variety of popular regression techniques (XGBoost, FC-MLP, Transformer, and LSTM) for multi-horizon, short-term forecasting of three variables (temperature, wind speed, and cloud cover) for multiple locations. During a 5-day live experiment, 4000 data sources were streamed for training and inferencing 144 models per hour. These models were parameterized to explore forecast error for two computational cost minimization methods: a novel auto-adaptive data reduction technique (Variance Horizon) and a performance-based concept drift-detection mechanism. Forecast error of all model variations were benchmarked in real-time against a state-of-the-art numerical weather prediction model. Performance was assessed using classical and novel evaluation metrics. Results indicate that using the Variance Horizon reduced computational usage by more than 50\%, while increasing between 0-15\% in error. Meanwhile, performance-based retraining reduced computational usage by up to 90\% while also improving forecast error by up to 10\%. Finally, the combination of both the Variance Horizon and performance-based retraining outperformed other model configurations by up to 99.7\% when considering error normalized to computational usage.

Stock Price Trend Prediction (SPTP) based on Limit Order Book (LOB) data is a fundamental challenge in financial markets. Despite advances in deep learning, existing models fail to generalize across different market conditions and struggle to reliably predict short-term trends. Surprisingly, by adapting a simple MLP-based architecture to LOB, we show that we surpass SoTA performance; thus, challenging the necessity of complex architectures. Unlike past work that shows robustness issues, we propose TLOB, a transformer-based model that uses a dual attention mechanism to capture spatial and temporal dependencies in LOB data. This allows it to adaptively focus on the market microstructure, making it particularly effective for longer-horizon predictions and volatile market conditions. We also introduce a new labeling method that improves on previous ones, removing the horizon bias. We evaluate TLOB's effectiveness using the established FI-2010 benchmark, which exceeds the state-of-the-art by an average of 3.7 F1-score(\%). Additionally, TLOB shows improvements on Tesla and Intel with a 1.3 and 7.7 increase in F1-score(\%), respectively. Additionally, we empirically show how stock price predictability has declined over time (-6.68 absolute points in F1-score(\%)), highlighting the growing market efficiencies. Predictability must be considered in relation to transaction costs, so we experimented with defining trends using an average spread, reflecting the primary transaction cost. The resulting performance deterioration underscores the complexity of translating trend classification into profitable trading strategies. We argue that our work provides new insights into the evolving landscape of stock price trend prediction and sets a strong foundation for future advancements in financial AI. We release the code at https://github.com/LeonardoBerti00/TLOB.

Time series forecasting holds significant importance in many real-world dynamic systems and has been extensively studied. Unlike natural language process (NLP) and computer vision (CV), where a single large model can tackle multiple tasks, models for time series forecasting are often specialized, necessitating distinct designs for different tasks and applications. While pre-trained foundation models have made impressive strides in NLP and CV, their development in time series domains has been constrained by data sparsity. Recent studies have revealed that large language models (LLMs) possess robust pattern recognition and reasoning abilities over complex sequences of tokens. However, the challenge remains in effectively aligning the modalities of time series data and natural language to leverage these capabilities. In this work, we present Time-LLM, a reprogramming framework to repurpose LLMs for general time series forecasting with the backbone language models kept intact. We begin by reprogramming the input time series with text prototypes before feeding it into the frozen LLM to align the two modalities. To augment the LLM's ability to reason with time series data, we propose Prompt-as-Prefix (PaP), which enriches the input context and directs the transformation of reprogrammed input patches. The transformed time series patches from the LLM are finally projected to obtain the forecasts. Our comprehensive evaluations demonstrate that Time-LLM is a powerful time series learner that outperforms state-of-the-art, specialized forecasting models. Moreover, Time-LLM excels in both few-shot and zero-shot learning scenarios.

Time series forecasting has attracted significant attention in recent decades. Previous studies have demonstrated that the Channel-Independent (CI) strategy improves forecasting performance by treating different channels individually, while it leads to poor generalization on unseen instances and ignores potentially necessary interactions between channels. Conversely, the Channel-Dependent (CD) strategy mixes all channels with even irrelevant and indiscriminate information, which, however, results in oversmoothing issues and limits forecasting accuracy. There is a lack of channel strategy that effectively balances individual channel treatment for improved forecasting performance without overlooking essential interactions between channels. Motivated by our observation of a correlation between the time series model's performance boost against channel mixing and the intrinsic similarity on a pair of channels, we developed a novel and adaptable Channel Clustering Module (CCM). CCM dynamically groups channels characterized by intrinsic similarities and leverages cluster information instead of individual channel identities, combining the best of CD and CI worlds. Extensive experiments on real-world datasets demonstrate that CCM can (1) boost the performance of CI and CD models by an average margin of 2.4% and 7.2% on long-term and short-term forecasting, respectively; (2) enable zero-shot forecasting with mainstream time series forecasting models; (3) uncover intrinsic time series patterns among channels and improve interpretability of complex time series models.

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of task-agnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (predict). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (refine). Notably, the generative performance of the model remains intact -- downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (synthesize).

Deep learning for time series forecasting has seen significant advancements over the past decades. However, despite the success of large-scale pre-training in language and vision domains, pre-trained time series models remain limited in scale and operate at a high cost, hindering the development of larger capable forecasting models in real-world applications. In response, we introduce Time-MoE, a scalable and unified architecture designed to pre-train larger, more capable forecasting foundation models while reducing inference costs. By leveraging a sparse mixture-of-experts (MoE) design, Time-MoE enhances computational efficiency by activating only a subset of networks for each prediction, reducing computational load while maintaining high model capacity. This allows Time-MoE to scale effectively without a corresponding increase in inference costs. Time-MoE comprises a family of decoder-only transformer models that operate in an auto-regressive manner and support flexible forecasting horizons with varying input context lengths. We pre-trained these models on our newly introduced large-scale data Time-300B, which spans over 9 domains and encompassing over 300 billion time points. For the first time, we scaled a time series foundation model up to 2.4 billion parameters, achieving significantly improved forecasting precision. Our results validate the applicability of scaling laws for training tokens and model size in the context of time series forecasting. Compared to dense models with the same number of activated parameters or equivalent computation budgets, our models consistently outperform them by large margin. These advancements position Time-MoE as a state-of-the-art solution for tackling real-world time series forecasting challenges with superior capability, efficiency, and flexibility.

We present Visuelle 2.0, the first dataset useful for facing diverse prediction problems that a fast-fashion company has to manage routinely. Furthermore, we demonstrate how the use of computer vision is substantial in this scenario. Visuelle 2.0 contains data for 6 seasons / 5355 clothing products of Nuna Lie, a famous Italian company with hundreds of shops located in different areas within the country. In particular, we focus on a specific prediction problem, namely short-observation new product sale forecasting (SO-fore). SO-fore assumes that the season has started and a set of new products is on the shelves of the different stores. The goal is to forecast the sales for a particular horizon, given a short, available past (few weeks), since no earlier statistics are available. To be successful, SO-fore approaches should capture this short past and exploit other modalities or exogenous data. To these aims, Visuelle 2.0 is equipped with disaggregated data at the item-shop level and multi-modal information for each clothing item, allowing computer vision approaches to come into play. The main message that we deliver is that the use of image data with deep networks boosts performances obtained when using the time series in long-term forecasting scenarios, ameliorating the WAPE and MAE by up to 5.48% and 7% respectively compared to competitive baseline methods. The dataset is available at https://humaticslab.github.io/forecasting/visuelle

Encouraged by decision makers' appetite for future information on topics ranging from elections to pandemics, and enabled by the explosion of data and computational methods, model based forecasts have garnered increasing influence on a breadth of decisions in modern society. Using several classic examples from fisheries management, I demonstrate that selecting the model or models that produce the most accurate and precise forecast (measured by statistical scores) can sometimes lead to worse outcomes (measured by real-world objectives). This can create a forecast trap, in which the outcomes such as fish biomass or economic yield decline while the manager becomes increasingly convinced that these actions are consistent with the best models and data available. The forecast trap is not unique to this example, but a fundamental consequence of non-uniqueness of models. Existing practices promoting a broader set of models are the best way to avoid the trap.

Accuracy and timeliness are indeed often conflicting goals in prediction tasks. Premature predictions may yield a higher rate of false alarms, whereas delaying predictions to gather more information can render them too late to be useful. In applications such as wildfires, crimes, and traffic jams, timely forecasting are vital for safeguarding human life and property. Consequently, finding a balance between accuracy and timeliness is crucial. In this paper, we propose an early spatio-temporal forecasting model based on Multi-Objective reinforcement learning that can either implement an optimal policy given a preference or infer the preference based on a small number of samples. The model addresses two primary challenges: 1) enhancing the accuracy of early forecasting and 2) providing the optimal policy for determining the most suitable prediction time for each area. Our method demonstrates superior performance on three large-scale real-world datasets, surpassing existing methods in early spatio-temporal forecasting tasks.

Time series forecasting plays a crucial role in data mining, driving rapid advancements across numerous industries. With the emergence of large models, time series foundation models (TSFMs) have exhibited remarkable generalization capabilities, such as zero-shot learning, through large-scale pre-training. Meanwhile, Retrieval-Augmented Generation (RAG) methods have been widely employed to enhance the performance of foundation models on unseen data, allowing models to access to external knowledge. In this paper, we introduce TimeRAF, a Retrieval-Augmented Forecasting model that enhance zero-shot time series forecasting through retrieval-augmented techniques. We develop customized time series knowledge bases that are tailored to the specific forecasting tasks. TimeRAF employs an end-to-end learnable retriever to extract valuable information from the knowledge base. Additionally, we propose Channel Prompting for knowledge integration, which effectively extracts relevant information from the retrieved knowledge along the channel dimension. Extensive experiments demonstrate the effectiveness of our model, showing significant improvement across various domains and datasets.

Deep learning has been actively applied to time series forecasting, leading to a deluge of new methods, belonging to the class of historical-value models. Yet, despite the attractive properties of time-index models, such as being able to model the continuous nature of underlying time series dynamics, little attention has been given to them. Indeed, while naive deep time-index models are far more expressive than the manually predefined function representations of classical time-index models, they are inadequate for forecasting, being unable to generalize to unseen time steps due to the lack of inductive bias. In this paper, we propose DeepTime, a meta-optimization framework to learn deep time-index models which overcome these limitations, yielding an efficient and accurate forecasting model. Extensive experiments on real world datasets in the long sequence time-series forecasting setting demonstrate that our approach achieves competitive results with state-of-the-art methods, and is highly efficient. Code is available at https://github.com/salesforce/DeepTime.

Graph-based deep learning methods have become popular tools to process collections of correlated time series. Differently from traditional multivariate forecasting methods, neural graph-based predictors take advantage of pairwise relationships by conditioning forecasts on a (possibly dynamic) graph spanning the time series collection. The conditioning can take the form of an architectural inductive bias on the neural forecasting architecture, resulting in a family of deep learning models called spatiotemporal graph neural networks. Such relational inductive biases enable the training of global forecasting models on large time-series collections, while at the same time localizing predictions w.r.t. each element in the set (i.e., graph nodes) by accounting for local correlations among them (i.e., graph edges). Indeed, recent theoretical and practical advances in graph neural networks and deep learning for time series forecasting make the adoption of such processing frameworks appealing and timely. However, most of the studies in the literature focus on proposing variations of existing neural architectures by taking advantage of modern deep learning practices, while foundational and methodological aspects have not been subject to systematic investigation. To fill the gap, this paper aims to introduce a comprehensive methodological framework that formalizes the forecasting problem and provides design principles for graph-based predictive models and methods to assess their performance. At the same time, together with an overview of the field, we provide design guidelines, recommendations, and best practices, as well as an in-depth discussion of open challenges and future research directions.

Recent efforts have been dedicated to enhancing time series forecasting accuracy by introducing advanced network architectures and self-supervised pretraining strategies. Nevertheless, existing approaches still exhibit two critical drawbacks. Firstly, these methods often rely on a single dataset for training, limiting the model's generalizability due to the restricted scale of the training data. Secondly, the one-step generation schema is widely followed, which necessitates a customized forecasting head and overlooks the temporal dependencies in the output series, and also leads to increased training costs under different horizon length settings. To address these issues, we propose a novel generative pretrained hierarchical transformer architecture for forecasting, named GPHT. There are two aspects of key designs in GPHT. On the one hand, we advocate for constructing a mixed dataset for pretraining our model, comprising various datasets from diverse data scenarios. This approach significantly expands the scale of training data, allowing our model to uncover commonalities in time series data and facilitating improved transfer to specific datasets. On the other hand, GPHT employs an auto-regressive forecasting approach under the channel-independent assumption, effectively modeling temporal dependencies in the output series. Importantly, no customized forecasting head is required, enabling a single model to forecast at arbitrary horizon settings. We conduct sufficient experiments on eight datasets with mainstream self-supervised pretraining models and supervised models. The results demonstrated that GPHT surpasses the baseline models across various fine-tuning and zero/few-shot learning settings in the traditional long-term forecasting task, providing support for verifying the feasibility of pretrained time series large models.

This study explores the integration of large language models (LLMs) into classic inflation nowcasting frameworks, particularly in light of high inflation volatility periods such as the COVID-19 pandemic. We propose InflaBERT, a BERT-based LLM fine-tuned to predict inflation-related sentiment in news. We use this model to produce NEWS, an index capturing the monthly sentiment of the news regarding inflation. Incorporating our expectation index into the Cleveland Fed's model, which is only based on macroeconomic autoregressive processes, shows a marginal improvement in nowcast accuracy during the pandemic. This highlights the potential of combining sentiment analysis with traditional economic indicators, suggesting further research to refine these methodologies for better real-time inflation monitoring. The source code is available at https://github.com/paultltc/InflaBERT.

This paper presents OLinear, a linear-based multivariate time series forecasting model that operates in an orthogonally transformed domain. Recent forecasting models typically adopt the temporal forecast (TF) paradigm, which directly encode and decode time series in the time domain. However, the entangled step-wise dependencies in series data can hinder the performance of TF. To address this, some forecasters conduct encoding and decoding in the transformed domain using fixed, dataset-independent bases (e.g., sine and cosine signals in the Fourier transform). In contrast, we utilize OrthoTrans, a data-adaptive transformation based on an orthogonal matrix that diagonalizes the series' temporal Pearson correlation matrix. This approach enables more effective encoding and decoding in the decorrelated feature domain and can serve as a plug-in module to enhance existing forecasters. To enhance the representation learning for multivariate time series, we introduce a customized linear layer, NormLin, which employs a normalized weight matrix to capture multivariate dependencies. Empirically, the NormLin module shows a surprising performance advantage over multi-head self-attention, while requiring nearly half the FLOPs. Extensive experiments on 24 benchmarks and 140 forecasting tasks demonstrate that OLinear consistently achieves state-of-the-art performance with high efficiency. Notably, as a plug-in replacement for self-attention, the NormLin module consistently enhances Transformer-based forecasters. The code and datasets are available at https://anonymous.4open.science/r/OLinear

Analysis and prediction of stock market time series data has attracted considerable interest from the research community over the last decade. Rapid development and evolution of sophisticated algorithms for statistical analysis of time series data, and availability of high-performance hardware has made it possible to process and analyze high volume stock market time series data effectively, in real-time. Among many other important characteristics and behavior of such data, forecasting is an area which has witnessed considerable focus. In this work, we have used time series of the index values of the Auto sector in India during January 2010 to December 2015 for a deeper understanding of the behavior of its three constituent components, e.g., the trend, the seasonal component, and the random component. Based on this structural analysis, we have also designed five approaches for forecasting and also computed their accuracy in prediction using suitably chosen training and test data sets. Extensive results are presented to demonstrate the effectiveness of our proposed decomposition approaches of time series and the efficiency of our forecasting techniques, even in presence of a random component and a sharply changing trend component in the time-series.

Time series forecasting traditionally relies on unimodal numerical inputs, which often struggle to capture high-level semantic patterns due to their dense and unstructured nature. While recent approaches have explored representing time series as text using large language models (LLMs), these methods remain limited by the discrete nature of token sequences and lack the perceptual intuition humans typically apply, such as interpreting visual patterns. In this paper, we propose a multimodal contrastive learning framework that transforms raw time series into structured visual and textual perspectives. Rather than using natural language or real-world images, we construct both modalities directly from numerical sequences. We then align these views in a shared semantic space via contrastive learning, enabling the model to capture richer and more complementary representations. Furthermore, we introduce a variate selection module that leverages the aligned representations to identify the most informative variables for multivariate forecasting. Extensive experiments on fifteen short-term and six long-term forecasting benchmarks demonstrate that our approach consistently outperforms strong unimodal and cross-modal baselines, highlighting the effectiveness of multimodal alignment in enhancing time series forecasting. Code is available at: https://github.com/Ironieser/TimesCLIP.

In a rapidly evolving job market, skill demand forecasting is crucial as it enables policymakers and businesses to anticipate and adapt to changes, ensuring that workforce skills align with market needs, thereby enhancing productivity and competitiveness. Additionally, by identifying emerging skill requirements, it directs individuals towards relevant training and education opportunities, promoting continuous self-learning and development. However, the absence of comprehensive datasets presents a significant challenge, impeding research and the advancement of this field. To bridge this gap, we present Job-SDF, a dataset designed to train and benchmark job-skill demand forecasting models. Based on 10.35 million public job advertisements collected from major online recruitment platforms in China between 2021 and 2023, this dataset encompasses monthly recruitment demand for 2,324 types of skills across 521 companies. Our dataset uniquely enables evaluating skill demand forecasting models at various granularities, including occupation, company, and regional levels. We benchmark a range of models on this dataset, evaluating their performance in standard scenarios, in predictions focused on lower value ranges, and in the presence of structural breaks, providing new insights for further research. Our code and dataset are publicly accessible via the https://github.com/Job-SDF/benchmark.

Foundation models have become increasingly popular for forecasting due to their ability to provide predictions without requiring a lot of training data. In this work, we demonstrate how TabPFN-v2, a general tabular foundation model, can be effectively applied to time series forecasting. We introduce TabPFN-TS, a simple method that combines TabPFN-v2 with lightweight feature engineering to enable both point and probabilistic forecasting. Despite its simplicity and compact size (11M parameters), TabPFN-TS achieves top rank on the public GIFT-Eval leaderboard in both forecasting tasks. Through ablation studies, we investigate factors contributing to this surprising effectiveness, especially considering TabPFN-v2 was pretrained solely on synthetic tabular data with no exposure to time series. Our results highlights the potential of tabular foundation models like TabPFN-v2 as a valuable new approach for time series forecasting. Our implementation is available at https://github.com/PriorLabs/tabpfn-time-series.

We examine the potential of ChatGPT and other large language models in predicting stock market returns using news headlines. We use ChatGPT to assess whether each headline is good, bad, or neutral for firms' stock prices. We document a significantly positive correlation between ChatGPT scores and subsequent daily stock returns. We find that ChatGPT outperforms traditional sentiment analysis methods. More basic models such as GPT-1, GPT-2, and BERT cannot accurately forecast returns, indicating return predictability is an emerging capacity of complex language models. Long-short strategies based on ChatGPT-4 deliver the highest Sharpe ratio. Furthermore, we find predictability in both small and large stocks, suggesting market underreaction to company news. Predictability is stronger among smaller stocks and stocks with bad news, consistent with limits-to-arbitrage also playing an important role. Finally, we propose a new method to evaluate and understand the models' reasoning capabilities. Overall, our results suggest that incorporating advanced language models into the investment decision-making process can yield more accurate predictions and enhance the performance of quantitative trading strategies.

As a branch of time series forecasting, stock movement forecasting is one of the challenging problems for investors and researchers. Since Transformer was introduced to analyze financial data, many researchers have dedicated themselves to forecasting stock movement using Transformer or attention mechanisms. However, existing research mostly focuses on individual stock information but ignores stock market information and high noise in stock data. In this paper, we propose a novel method using the attention mechanism in which both stock market information and individual stock information are considered. Meanwhile, we propose a novel EMD-based algorithm for reducing short-term noise in stock data. Two randomly selected exchange-traded funds (ETFs) spanning over ten years from US stock markets are used to demonstrate the superior performance of the proposed attention-based method. The experimental analysis demonstrates that the proposed attention-based method significantly outperforms other state-of-the-art baselines. Code is available at https://github.com/DurandalLee/ACEFormer.

Financial forecasting has been an important and active area of machine learning research because of the challenges it presents and the potential rewards that even minor improvements in prediction accuracy or forecasting may entail. Traditionally, financial forecasting has heavily relied on quantitative indicators and metrics derived from structured financial statements. Earnings conference call data, including text and audio, is an important source of unstructured data that has been used for various prediction tasks using deep earning and related approaches. However, current deep learning-based methods are limited in the way that they deal with numeric data; numbers are typically treated as plain-text tokens without taking advantage of their underlying numeric structure. This paper describes a numeric-oriented hierarchical transformer model to predict stock returns, and financial risk using multi-modal aligned earnings calls data by taking advantage of the different categories of numbers (monetary, temporal, percentages etc.) and their magnitude. We present the results of a comprehensive evaluation of NumHTML against several state-of-the-art baselines using a real-world publicly available dataset. The results indicate that NumHTML significantly outperforms the current state-of-the-art across a variety of evaluation metrics and that it has the potential to offer significant financial gains in a practical trading context.

The present document delineates the analysis, design, implementation, and benchmarking of various neural network architectures within a short-term frequency prediction system for the foreign exchange market (FOREX). Our aim is to simulate the judgment of the human expert (technical analyst) using a system that responds promptly to changes in market conditions, thus enabling the optimization of short-term trading strategies. We designed and implemented a series of LSTM neural network architectures which are taken as input the exchange rate values and generate the short-term market trend forecasting signal and an ANN custom architecture based on technical analysis indicator simulators We performed a comparative analysis of the results and came to useful conclusions regarding the suitability of each architecture and the cost in terms of time and computational power to implement them. The ANN custom architecture produces better prediction quality with higher sensitivity using fewer resources and spending less time than LSTM architectures. The ANN custom architecture appears to be ideal for use in low-power computing systems and for use cases that need fast decisions with the least possible computational cost.

Ensembling is among the most popular tools in machine learning (ML) due to its effectiveness in minimizing variance and thus improving generalization. Most ensembling methods for black-box base learners fall under the umbrella of "stacked generalization," namely training an ML algorithm that takes the inferences from the base learners as input. While stacking has been widely applied in practice, its theoretical properties are poorly understood. In this paper, we prove a novel result, showing that choosing the best stacked generalization from a (finite or finite-dimensional) family of stacked generalizations based on cross-validated performance does not perform "much worse" than the oracle best. Our result strengthens and significantly extends the results in Van der Laan et al. (2007). Inspired by the theoretical analysis, we further propose a particular family of stacked generalizations in the context of probabilistic forecasting, each one with a different sensitivity for how much the ensemble weights are allowed to vary across items, timestamps in the forecast horizon, and quantiles. Experimental results demonstrate the performance gain of the proposed method.

Model selection is a critical step in time series forecasting, traditionally requiring extensive performance evaluations across various datasets. Meta-learning approaches aim to automate this process, but they typically depend on pre-constructed performance matrices, which are costly to build. In this work, we propose to leverage Large Language Models (LLMs) as a lightweight alternative for model selection. Our method eliminates the need for explicit performance matrices by utilizing the inherent knowledge and reasoning capabilities of LLMs. Through extensive experiments with LLaMA, GPT and Gemini, we demonstrate that our approach outperforms traditional meta-learning techniques and heuristic baselines, while significantly reducing computational overhead. These findings underscore the potential of LLMs in efficient model selection for time series forecasting.

We present Timer-XL, a generative Transformer for unified time series forecasting. To uniformly predict 1D and 2D time series, we generalize next token prediction, predominantly adopted for causal generation of 1D sequences, to multivariate next token prediction. The proposed paradigm uniformly formulates various forecasting scenarios as a long-context generation problem. We opt for the generative Transformer, which can capture global-range and causal dependencies while providing contextual flexibility, to implement unified forecasting on univariate series characterized by non-stationarity, multivariate time series with complicated dynamics and correlations, and covariate-informed contexts that include both endogenous and exogenous variables. Technically, we propose a universal TimeAttention to facilitate generative Transformers on time series, which can effectively capture fine-grained intra- and inter-series dependencies of flattened time series tokens (patches) and is further strengthened by position embeddings in both temporal and variable dimensions. Timer-XL achieves state-of-the-art performance across challenging forecasting benchmarks through a unified approach. As a large time series model, it demonstrates notable model transferability by large-scale pre-training, as well as contextual flexibility in token lengths, positioning it as a one-for-all forecaster.

We introduce TimeMCL, a method leveraging the Multiple Choice Learning (MCL) paradigm to forecast multiple plausible time series futures. Our approach employs a neural network with multiple heads and utilizes the Winner-Takes-All (WTA) loss to promote diversity among predictions. MCL has recently gained attention due to its simplicity and ability to address ill-posed and ambiguous tasks. We propose an adaptation of this framework for time-series forecasting, presenting it as an efficient method to predict diverse futures, which we relate to its implicit quantization objective. We provide insights into our approach using synthetic data and evaluate it on real-world time series, demonstrating its promising performance at a light computational cost.

As the Chinese stock market continues to evolve and its market structure grows increasingly complex, traditional quantitative trading methods are facing escalating challenges. Particularly, due to policy uncertainty and the frequent market fluctuations triggered by sudden economic events, existing models often struggle to accurately predict market dynamics. To address these challenges, this paper introduces Stockformer, a price-volume factor stock selection model that integrates wavelet transformation and a multitask self-attention network, aimed at enhancing responsiveness and predictive accuracy regarding market instabilities. Through discrete wavelet transform, Stockformer decomposes stock returns into high and low frequencies, meticulously capturing long-term market trends and short-term fluctuations, including abrupt events. Moreover, the model incorporates a Dual-Frequency Spatiotemporal Encoder and graph embedding techniques to effectively capture complex temporal and spatial relationships among stocks. Employing a multitask learning strategy, it simultaneously predicts stock returns and directional trends. Experimental results show that Stockformer outperforms existing advanced methods on multiple real stock market datasets. In strategy backtesting, Stockformer consistently demonstrates exceptional stability and reliability across market conditions-whether rising, falling, or fluctuating-particularly maintaining high performance during downturns or volatile periods, indicating a high adaptability to market fluctuations. To foster innovation and collaboration in the financial analysis sector, the Stockformer model's code has been open-sourced and is available on the GitHub repository: https://github.com/Eric991005/Multitask-Stockformer.

Planning safe robot motions in the presence of humans requires reliable forecasts of future human motion. However, simply predicting the most likely motion from prior interactions does not guarantee safety. Such forecasts fail to model the long tail of possible events, which are rarely observed in limited datasets. On the other hand, planning for worst-case motions leads to overtly conservative behavior and a "frozen robot". Instead, we aim to learn forecasts that predict counterfactuals that humans guard against. We propose a novel game-theoretic framework for joint planning and forecasting with the payoff being the performance of the planner against the demonstrator, and present practical algorithms to train models in an end-to-end fashion. We demonstrate that our proposed algorithm results in safer plans in a crowd navigation simulator and real-world datasets of pedestrian motion. We release our code at https://github.com/portal-cornell/Game-Theoretic-Forecasting-Planning.

In recent years, the introduction of self-supervised contrastive learning (SSCL) has demonstrated remarkable improvements in representation learning across various domains, including natural language processing and computer vision. By leveraging the inherent benefits of self-supervision, SSCL enables the pre-training of representation models using vast amounts of unlabeled data. Despite these advances, there remains a significant gap in understanding the impact of different SSCL strategies on time series forecasting performance, as well as the specific benefits that SSCL can bring. This paper aims to address these gaps by conducting a comprehensive analysis of the effectiveness of various training variables, including different SSCL algorithms, learning strategies, model architectures, and their interplay. Additionally, to gain deeper insights into the improvements brought about by SSCL in the context of time-series forecasting, a qualitative analysis of the empirical receptive field is performed. Through our experiments, we demonstrate that the end-to-end training of a Transformer model using the Mean Squared Error (MSE) loss and SSCL emerges as the most effective approach in time series forecasting. Notably, the incorporation of the contrastive objective enables the model to prioritize more pertinent information for forecasting, such as scale and periodic relationships. These findings contribute to a better understanding of the benefits of SSCL in time series forecasting and provide valuable insights for future research in this area. Our codes are available at https://github.com/chiyuzhang94/contrastive_learning_time-series_e2e.

Deep learning for time series forecasting has traditionally operated within a one-model-per-dataset framework, limiting its potential to leverage the game-changing impact of large pre-trained models. The concept of universal forecasting, emerging from pre-training on a vast collection of time series datasets, envisions a single Large Time Series Model capable of addressing diverse downstream forecasting tasks. However, constructing such a model poses unique challenges specific to time series data: i) cross-frequency learning, ii) accommodating an arbitrary number of variates for multivariate time series, and iii) addressing the varying distributional properties inherent in large-scale data. To address these challenges, we present novel enhancements to the conventional time series Transformer architecture, resulting in our proposed Masked Encoder-based Universal Time Series Forecasting Transformer (Moirai). Trained on our newly introduced Large-scale Open Time Series Archive (LOTSA) featuring over 27B observations across nine domains, Moirai achieves competitive or superior performance as a zero-shot forecaster when compared to full-shot models. Code, model weights, and data will be released.

We focus on solving the univariate times series point forecasting problem using deep learning. We propose a deep neural architecture based on backward and forward residual links and a very deep stack of fully-connected layers. The architecture has a number of desirable properties, being interpretable, applicable without modification to a wide array of target domains, and fast to train. We test the proposed architecture on several well-known datasets, including M3, M4 and TOURISM competition datasets containing time series from diverse domains. We demonstrate state-of-the-art performance for two configurations of N-BEATS for all the datasets, improving forecast accuracy by 11% over a statistical benchmark and by 3% over last year's winner of the M4 competition, a domain-adjusted hand-crafted hybrid between neural network and statistical time series models. The first configuration of our model does not employ any time-series-specific components and its performance on heterogeneous datasets strongly suggests that, contrarily to received wisdom, deep learning primitives such as residual blocks are by themselves sufficient to solve a wide range of forecasting problems. Finally, we demonstrate how the proposed architecture can be augmented to provide outputs that are interpretable without considerable loss in accuracy.

Competitions play an invaluable role in the field of forecasting, as exemplified through the recent M4 competition. The competition received attention from both academics and practitioners and sparked discussions around the representativeness of the data for business forecasting. Several competitions featuring real-life business forecasting tasks on the Kaggle platform has, however, been largely ignored by the academic community. We believe the learnings from these competitions have much to offer to the forecasting community and provide a review of the results from six Kaggle competitions. We find that most of the Kaggle datasets are characterized by higher intermittence and entropy than the M-competitions and that global ensemble models tend to outperform local single models. Furthermore, we find the strong performance of gradient boosted decision trees, increasing success of neural networks for forecasting, and a variety of techniques for adapting machine learning models to the forecasting task.

Urgent care clinics and emergency departments around the world periodically suffer from extended wait times beyond patient expectations due to inadequate staffing levels. These delays have been linked with adverse clinical outcomes. Previous research into forecasting demand this domain has mostly used a collection of statistical techniques, with machine learning approaches only now beginning to emerge in recent literature. The forecasting problem for this domain is difficult and has also been complicated by the COVID-19 pandemic which has introduced an additional complexity to this estimation due to typical demand patterns being disrupted. This study explores the ability of machine learning methods to generate accurate patient presentations at two large urgent care clinics located in Auckland, New Zealand. A number of machine learning algorithms were explored in order to determine the most effective technique for this problem domain, with the task of making forecasts of daily patient demand three months in advance. The study also performed an in-depth analysis into the model behaviour in respect to the exploration of which features are most effective at predicting demand and which features are capable of adaptation to the volatility caused by the COVID-19 pandemic lockdowns. The results showed that ensemble-based methods delivered the most accurate and consistent solutions on average, generating improvements in the range of 23%-27% over the existing in-house methods for estimating the daily demand.

Introduction: The paper addresses the challenging problem of predicting the short-term realized volatility of the Bitcoin price using order flow information. The inherent stochastic nature and anti-persistence of price pose difficulties in accurate prediction. Methods: To address this, we propose a method that transforms order flow data over a fixed time interval (snapshots) into images. The order flow includes trade sizes, trade directions, and limit order book, and is mapped into image colour channels. These images are then used to train both a simple 3-layer Convolutional Neural Network (CNN) and more advanced ResNet-18 and ConvMixer, with additionally supplementing them with hand-crafted features. The models are evaluated against classical GARCH, Multilayer Perceptron trained on raw data, and a naive guess method that considers current volatility as a prediction. Results: The experiments are conducted using price data from January 2021 and evaluate model performance in terms of root mean square error (RMSPE). The results show that our order flow representation with a CNN as a predictive model achieves the best performance, with an RMSPE of 0.85+/-1.1 for the model with aggregated features and 1.0+/-1.4 for the model without feature supplementation. ConvMixer with feature supplementation follows closely. In comparison, the RMSPE for the naive guess method was 1.4+/-3.0.

Recent innovations in transformers have shown their superior performance in natural language processing (NLP) and computer vision (CV). The ability to capture long-range dependencies and interactions in sequential data has also triggered a great interest in time series modeling, leading to the widespread use of transformers in many time series applications. However, being the most common and crucial application, the adaptation of transformers to time series forecasting has remained limited, with both promising and inconsistent results. In contrast to the challenges in NLP and CV, time series problems not only add the complexity of order or temporal dependence among input sequences but also consider trend, level, and seasonality information that much of this data is valuable for decision making. The conventional training scheme has shown deficiencies regarding model overfitting, data scarcity, and privacy issues when working with transformers for a forecasting task. In this work, we propose attentive federated transformers for time series stock forecasting with better performance while preserving the privacy of participating enterprises. Empirical results on various stock data from the Yahoo! Finance website indicate the superiority of our proposed scheme in dealing with the above challenges and data heterogeneity in federated learning.

Current deep learning models for dynamics forecasting struggle with generalization. They can only forecast in a specific domain and fail when applied to systems with different parameters, external forces, or boundary conditions. We propose a model-based meta-learning method called DyAd which can generalize across heterogeneous domains by partitioning them into different tasks. DyAd has two parts: an encoder which infers the time-invariant hidden features of the task with weak supervision, and a forecaster which learns the shared dynamics of the entire domain. The encoder adapts and controls the forecaster during inference using adaptive instance normalization and adaptive padding. Theoretically, we prove that the generalization error of such procedure is related to the task relatedness in the source domain, as well as the domain differences between source and target. Experimentally, we demonstrate that our model outperforms state-of-the-art approaches on both turbulent flow and real-world ocean data forecasting tasks.

This study develops FinText, a financial word embedding compiled from 15 years of business news archives. The results show that FinText produces substantially more accurate results than general word embeddings based on the gold-standard financial benchmark we introduced. In contrast to well-known econometric models, and over the sample period from 27 July 2007 to 27 January 2022 for 23 NASDAQ stocks, using stock-related news, our simple natural language processing model supported by different word embeddings improves realised volatility forecasts on high volatility days. This improvement in realised volatility forecasting performance switches to normal volatility days when general hot news is used. By utilising SHAP, an Explainable AI method, we also identify and classify key phrases in stock-related and general hot news that moved volatility.

Time-series forecasting is one of the most active research topics in artificial intelligence. Applications in real-world time series should consider two factors for achieving reliable predictions: modeling dynamic dependencies among multiple variables and adjusting the model's intrinsic hyperparameters. A still open gap in that literature is that statistical and ensemble learning approaches systematically present lower predictive performance than deep learning methods. They generally disregard the data sequence aspect entangled with multivariate data represented in more than one time series. Conversely, this work presents a novel neural network architecture for time-series forecasting that combines the power of graph evolution with deep recurrent learning on distinct data distributions; we named our method Recurrent Graph Evolution Neural Network (ReGENN). The idea is to infer multiple multivariate relationships between co-occurring time-series by assuming that the temporal data depends not only on inner variables and intra-temporal relationships (i.e., observations from itself) but also on outer variables and inter-temporal relationships (i.e., observations from other-selves). An extensive set of experiments was conducted comparing ReGENN with dozens of ensemble methods and classical statistical ones, showing sound improvement of up to 64.87% over the competing algorithms. Furthermore, we present an analysis of the intermediate weights arising from ReGENN, showing that by looking at inter and intra-temporal relationships simultaneously, time-series forecasting is majorly improved if paying attention to how multiple multivariate data synchronously evolve.

Vaccine supply chain optimization can benefit from hierarchical time series forecasting, when grouping the vaccines by type or location. However, forecasts of different hierarchy levels become incoherent when higher levels do not match the sum of the lower levels forecasts, which can be addressed by reconciliation methods. In this paper, we tackle the vaccine sale forecasting problem by modeling sales data from GSK between 2010 and 2021 as a hierarchical time series. After forecasting future values with several ARIMA models, we systematically compare the performance of various reconciliation methods, using statistical tests. We also compare the performance of the forecast before and after COVID. The results highlight Minimum Trace and Weighted Least Squares with Structural scaling as the best performing methods, which provided a coherent forecast while reducing the forecast error of the baseline ARIMA.

Time series forecasting is an important and forefront task in many real-world applications. However, most of time series forecasting techniques assume that the training data is clean without anomalies. This assumption is unrealistic since the collected time series data can be contaminated in practice. The forecasting model will be inferior if it is directly trained by time series with anomalies. Thus it is essential to develop methods to automatically learn a robust forecasting model from the contaminated data. In this paper, we first statistically define three types of anomalies, then theoretically and experimentally analyze the loss robustness and sample robustness when these anomalies exist. Based on our analyses, we propose a simple and efficient algorithm to learn a robust forecasting model. Extensive experiments show that our method is highly robust and outperforms all existing approaches. The code is available at https://github.com/haochenglouis/RobustTSF.

This paper introduces the FinSen dataset that revolutionizes financial market analysis by integrating economic and financial news articles from 197 countries with stock market data. The dataset's extensive coverage spans 15 years from 2007 to 2023 with temporal information, offering a rich, global perspective with 160,000 records on financial market news. Our study leverages causally validated sentiment scores and LSTM models to enhance market forecast accuracy and reliability. Utilizing the FinSen dataset, we introduce an innovative Focal Calibration Loss, reducing Expected Calibration Error (ECE) to 3.34 percent with the DAN 3 model. This not only improves prediction accuracy but also aligns probabilistic forecasts closely with real outcomes, crucial for the financial sector where predicted probability is paramount. Our approach demonstrates the effectiveness of combining sentiment analysis with precise calibration techniques for trustworthy financial forecasting where the cost of misinterpretation can be high. Finsen Data can be found at [this github URL](https://github.com/EagleAdelaide/FinSen_Dataset.git).

In-context learning, the ability of large language models to perform tasks using only examples provided in the prompt, has recently been adapted for time series forecasting. This paradigm enables zero-shot prediction, where past values serve as context for forecasting future values, making powerful forecasting tools accessible to non-experts and increasing the performance when training data are scarce. Most existing zero-shot forecasting approaches rely on transformer architectures, which, despite their success in language, often fall short of expectations in time series forecasting, where recurrent models like LSTMs frequently have the edge. Conversely, while LSTMs are well-suited for time series modeling due to their state-tracking capabilities, they lack strong in-context learning abilities. We introduce TiRex that closes this gap by leveraging xLSTM, an enhanced LSTM with competitive in-context learning skills. Unlike transformers, state-space models, or parallelizable RNNs such as RWKV, TiRex retains state-tracking, a critical property for long-horizon forecasting. To further facilitate its state-tracking ability, we propose a training-time masking strategy called CPM. TiRex sets a new state of the art in zero-shot time series forecasting on the HuggingFace benchmarks GiftEval and Chronos-ZS, outperforming significantly larger models including TabPFN-TS (Prior Labs), Chronos Bolt (Amazon), TimesFM (Google), and Moirai (Salesforce) across both short- and long-term forecasts.

Bitcoin, with its ever-growing popularity, has demonstrated extreme price volatility since its origin. This volatility, together with its decentralised nature, make Bitcoin highly subjective to speculative trading as compared to more traditional assets. In this paper, we propose a multimodal model for predicting extreme price fluctuations. This model takes as input a variety of correlated assets, technical indicators, as well as Twitter content. In an in-depth study, we explore whether social media discussions from the general public on Bitcoin have predictive power for extreme price movements. A dataset of 5,000 tweets per day containing the keyword `Bitcoin' was collected from 2015 to 2021. This dataset, called PreBit, is made available online. In our hybrid model, we use sentence-level FinBERT embeddings, pretrained on financial lexicons, so as to capture the full contents of the tweets and feed it to the model in an understandable way. By combining these embeddings with a Convolutional Neural Network, we built a predictive model for significant market movements. The final multimodal ensemble model includes this NLP model together with a model based on candlestick data, technical indicators and correlated asset prices. In an ablation study, we explore the contribution of the individual modalities. Finally, we propose and backtest a trading strategy based on the predictions of our models with varying prediction threshold and show that it can used to build a profitable trading strategy with a reduced risk over a `hold' or moving average strategy.

One of the most discussed problems in the financial world is stock option pricing. The Black-Scholes Equation is a Parabolic Partial Differential Equation which provides an option pricing model. The present work proposes an approach based on Neural Networks to solve the Black-Scholes Equations. Real-world data from the stock options market were used as the initial boundary to solve the Black-Scholes Equation. In particular, times series of call options prices of Brazilian companies Petrobras and Vale were employed. The results indicate that the network can learn to solve the Black-Sholes Equation for a specific real-world stock options time series. The experimental results showed that the Neural network option pricing based on the Black-Sholes Equation solution can reach an option pricing forecasting more accurate than the traditional Black-Sholes analytical solutions. The experimental results making it possible to use this methodology to make short-term call option price forecasts in options markets.

The paper studies the linear model for Bitcoin price which includes regression features based on Bitcoin currency statistics, mining processes, Google search trends, Wikipedia pages visits. The pattern of deviation of regression model prediction from real prices is simpler comparing to price time series. It is assumed that this pattern can be predicted by an experienced expert. In such a way, using the combination of the regression model and expert correction, one can receive better results than with either regression model or expert opinion only. It is shown that Bayesian approach makes it possible to utilize the probabilistic approach using distributions with fat tails and take into account the outliers in Bitcoin price time series.

Online updating of time series forecasting models aims to address the concept drifting problem by efficiently updating forecasting models based on streaming data. Many algorithms are designed for online time series forecasting, with some exploiting cross-variable dependency while others assume independence among variables. Given every data assumption has its own pros and cons in online time series modeling, we propose Online ensembling Network (OneNet). It dynamically updates and combines two models, with one focusing on modeling the dependency across the time dimension and the other on cross-variate dependency. Our method incorporates a reinforcement learning-based approach into the traditional online convex programming framework, allowing for the linear combination of the two models with dynamically adjusted weights. OneNet addresses the main shortcoming of classical online learning methods that tend to be slow in adapting to the concept drift. Empirical results show that OneNet reduces online forecasting error by more than 50% compared to the State-Of-The-Art (SOTA) method. The code is available at https://github.com/yfzhang114/OneNet.

Deep models have demonstrated remarkable performance in time series forecasting. However, due to the partially-observed nature of real-world applications, solely focusing on the target of interest, so-called endogenous variables, is usually insufficient to guarantee accurate forecasting. Notably, a system is often recorded into multiple variables, where the exogenous variables can provide valuable external information for endogenous variables. Thus, unlike well-established multivariate or univariate forecasting paradigms that either treat all the variables equally or ignore exogenous information, this paper focuses on a more practical setting: time series forecasting with exogenous variables. We propose a novel approach, TimeXer, to ingest external information to enhance the forecasting of endogenous variables. With deftly designed embedding layers, TimeXer empowers the canonical Transformer with the ability to reconcile endogenous and exogenous information, where patch-wise self-attention and variate-wise cross-attention are used simultaneously. Moreover, global endogenous tokens are learned to effectively bridge the causal information underlying exogenous series into endogenous temporal patches. Experimentally, TimeXer achieves consistent state-of-the-art performance on twelve real-world forecasting benchmarks and exhibits notable generality and scalability. Code is available at this repository: https://github.com/thuml/TimeXer.

Time series analysis and forecasting of stock market prices has been a very active area of research over the last two decades. Availability of extremely fast and parallel architecture of computing and sophisticated algorithms has made it possible to extract, store, process and analyze high volume stock market time series data very efficiently. In this paper, we have used time series data of the two sectors of the Indian economy: Information Technology and Capital Goods for the period January 2009 till April 2016 and have studied the relationships of these two time series with the time series of DJIA index, NIFTY index and the US Dollar to Indian Rupee exchange rate. We establish by graphical and statistical tests that while the IT sector of India has a strong association with DJIA index and the Dollar to Rupee exchange rate, the Indian CG sector exhibits a strong association with the NIFTY index. We contend that these observations corroborate our hypotheses that the Indian IT sector is strongly coupled with the world economy whereas the CG sector of India reflects internal economic growth of India. We also present several models of regression between the time series which exhibit strong association among them. The effectiveness of these models have been demonstrated by very low values of their forecasting errors.

Forecasting future world events is a challenging but valuable task. Forecasts of climate, geopolitical conflict, pandemics and economic indicators help shape policy and decision making. In these domains, the judgment of expert humans contributes to the best forecasts. Given advances in language modeling, can these forecasts be automated? To this end, we introduce Autocast, a dataset containing thousands of forecasting questions and an accompanying news corpus. Questions are taken from forecasting tournaments, ensuring high quality, real-world importance, and diversity. The news corpus is organized by date, allowing us to precisely simulate the conditions under which humans made past forecasts (avoiding leakage from the future). Motivated by the difficulty of forecasting numbers across orders of magnitude (e.g. global cases of COVID-19 in 2022), we also curate IntervalQA, a dataset of numerical questions and metrics for calibration. We test language models on our forecasting task and find that performance is far below a human expert baseline. However, performance improves with increased model size and incorporation of relevant information from the news corpus. In sum, Autocast poses a novel challenge for large language models and improved performance could bring large practical benefits.

Ancillaries have become a major source of revenue and profitability in the travel industry. Yet, conventional pricing strategies are based on business rules that are poorly optimized and do not respond to changing market conditions. This paper describes the dynamic pricing model developed by Deepair solutions, an AI technology provider for travel suppliers. We present a pricing model that provides dynamic pricing recommendations specific to each customer interaction and optimizes expected revenue per customer. The unique nature of personalized pricing provides the opportunity to search over the market space to find the optimal price-point of each ancillary for each customer, without violating customer privacy. In this paper, we present and compare three approaches for dynamic pricing of ancillaries, with increasing levels of sophistication: (1) a two-stage forecasting and optimization model using a logistic mapping function; (2) a two-stage model that uses a deep neural network for forecasting, coupled with a revenue maximization technique using discrete exhaustive search; (3) a single-stage end-to-end deep neural network that recommends the optimal price. We describe the performance of these models based on both offline and online evaluations. We also measure the real-world business impact of these approaches by deploying them in an A/B test on an airline's internet booking website. We show that traditional machine learning techniques outperform human rule-based approaches in an online setting by improving conversion by 36% and revenue per offer by 10%. We also provide results for our offline experiments which show that deep learning algorithms outperform traditional machine learning techniques for this problem. Our end-to-end deep learning model is currently being deployed by the airline in their booking system.

Deep learning and pre-trained models have shown great success in time series forecasting. However, in the tourism industry, time series data often exhibit a leading time property, presenting a 2D structure. This introduces unique challenges for forecasting in this sector. In this study, we propose a novel modelling paradigm, TripCast, which treats trip time series as 2D data and learns representations through masking and reconstruction processes. Pre-trained on large-scale real-world data, TripCast notably outperforms other state-of-the-art baselines in in-domain forecasting scenarios and demonstrates strong scalability and transferability in out-domain forecasting scenarios.

Time Series Forecasting has been an active area of research due to its many applications ranging from network usage prediction, resource allocation, anomaly detection, and predictive maintenance. Numerous publications published in the last five years have proposed diverse sets of objective loss functions to address cases such as biased data, long-term forecasting, multicollinear features, etc. In this paper, we have summarized 14 well-known regression loss functions commonly used for time series forecasting and listed out the circumstances where their application can aid in faster and better model convergence. We have also demonstrated how certain categories of loss functions perform well across all data sets and can be considered as a baseline objective function in circumstances where the distribution of the data is unknown. Our code is available at GitHub: https://github.com/aryan-jadon/Regression-Loss-Functions-in-Time-Series-Forecasting-Tensorflow.

While large language models have rapidly evolved towards general artificial intelligence, their versatility in analyzing time series data remains limited. To address this limitation, we propose a novel normalization technique that considers the inherent nature of tokenization. The proposed Tokenization-Optimized Normalization (TOKON) simplifies time series data by representing each element with a single token, effectively reducing the number of tokens by 2 to 3 times. Additionally, we introduce a novel prompt for time series forecasting, termed Time Series Forecasting with Care (TFSC), to further enhance forecasting performance. Experimental results demonstrate that TOKON improves root mean square error (RMSE) for multi-step forecasting by approximately 7% to 18%, depending on the dataset and prompting method. Furthermore, TFSC, when used in conjunction with TOKON, shows additional improvements in forecasting accuracy for certain datasets

Accurately predicting the future would be an important milestone in the capabilities of artificial intelligence. However, research on the ability of large language models to provide probabilistic predictions about future events remains nascent. To empirically test this ability, we enrolled OpenAI's state-of-the-art large language model, GPT-4, in a three-month forecasting tournament hosted on the Metaculus platform. The tournament, running from July to October 2023, attracted 843 participants and covered diverse topics including Big Tech, U.S. politics, viral outbreaks, and the Ukraine conflict. Focusing on binary forecasts, we show that GPT-4's probabilistic forecasts are significantly less accurate than the median human-crowd forecasts. We find that GPT-4's forecasts did not significantly differ from the no-information forecasting strategy of assigning a 50% probability to every question. We explore a potential explanation, that GPT-4 might be predisposed to predict probabilities close to the midpoint of the scale, but our data do not support this hypothesis. Overall, we find that GPT-4 significantly underperforms in real-world predictive tasks compared to median human-crowd forecasts. A potential explanation for this underperformance is that in real-world forecasting tournaments, the true answers are genuinely unknown at the time of prediction; unlike in other benchmark tasks like professional exams or time series forecasting, where strong performance may at least partly be due to the answers being memorized from the training data. This makes real-world forecasting tournaments an ideal environment for testing the generalized reasoning and prediction capabilities of artificial intelligence going forward.

Portfolio optimization has been a broad and intense area of interest for quantitative and statistical finance researchers and financial analysts. It is a challenging task to design a portfolio of stocks to arrive at the optimized values of the return and risk. This paper presents an algorithmic approach for designing optimum risk and eigen portfolios for five thematic sectors of the NSE of India. The prices of the stocks are extracted from the web from Jan 1, 2016, to Dec 31, 2020. Optimum risk and eigen portfolios for each sector are designed based on ten critical stocks from the sector. An LSTM model is designed for predicting future stock prices. Seven months after the portfolios were formed, on Aug 3, 2021, the actual returns of the portfolios are compared with the LSTM-predicted returns. The predicted and the actual returns indicate a very high-level accuracy of the LSTM model.

We introduce Toto, a time series forecasting foundation model with 151 million parameters. Toto uses a modern decoder-only architecture coupled with architectural innovations designed to account for specific challenges found in multivariate observability time series data. Toto's pre-training corpus is a mixture of observability data, open datasets, and synthetic data, and is 4-10times larger than those of leading time series foundation models. Additionally, we introduce BOOM, a large-scale benchmark consisting of 350 million observations across 2,807 real-world time series. For both Toto and BOOM, we source observability data exclusively from Datadog's own telemetry and internal observability metrics. Extensive evaluations demonstrate that Toto achieves state-of-the-art performance on both BOOM and on established general purpose time series forecasting benchmarks. Toto's model weights, inference code, and evaluation scripts, as well as BOOM's data and evaluation code, are all available as open source under the Apache 2.0 License available at https://huggingface.co/Datadog/Toto-Open-Base-1.0 and https://github.com/DataDog/toto.

Recent studies have demonstrated the great power of Transformer models for time series forecasting. One of the key elements that lead to the transformer's success is the channel-independent (CI) strategy to improve the training robustness. However, the ignorance of the correlation among different channels in CI would limit the model's forecasting capacity. In this work, we design a special Transformer, i.e., Channel Aligned Robust Blend Transformer (CARD for short), that addresses key shortcomings of CI type Transformer in time series forecasting. First, CARD introduces a channel-aligned attention structure that allows it to capture both temporal correlations among signals and dynamical dependence among multiple variables over time. Second, in order to efficiently utilize the multi-scale knowledge, we design a token blend module to generate tokens with different resolutions. Third, we introduce a robust loss function for time series forecasting to alleviate the potential overfitting issue. This new loss function weights the importance of forecasting over a finite horizon based on prediction uncertainties. Our evaluation of multiple long-term and short-term forecasting datasets demonstrates that CARD significantly outperforms state-of-the-art time series forecasting methods. The code is available at the following repository:https://github.com/wxie9/CARD

In quantitative finance, machine learning methods are essential for alpha generation. This study introduces a new approach that combines Hidden Markov Models (HMM) and neural networks, integrated with Black-Litterman portfolio optimization. During the COVID period (2019-2022), this dual-model approach achieved a 83% return with a Sharpe ratio of 0.77. It incorporates two risk models to enhance risk management, showing efficiency during volatile periods. The methodology was implemented on the QuantConnect platform, which was chosen for its robust framework and experimental reproducibility. The system, which predicts future price movements, includes a three-year warm-up to ensure proper algorithm function. It targets highly liquid, large-cap energy stocks to ensure stable and predictable performance while also considering broker payments. The dual-model alpha system utilizes log returns to select the optimal state based on the historical performance. It combines state predictions with neural network outputs, which are based on historical data, to generate trading signals. This study examined the architecture of the trading system, data pre-processing, training, and performance. The full code and backtesting data are available under the QuantConnect terms.

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's individually, and do not leverage the dynamic distributions underlying the MTS's, leading to sub-optimal results when the sparsity is high. To address this challenge, we propose a novel generative model, which tracks the transition of latent clusters, instead of isolated feature representations, to achieve robust modeling. It is characterized by a newly designed dynamic Gaussian mixture distribution, which captures the dynamics of clustering structures, and is used for emitting timeseries. The generative model is parameterized by neural networks. A structured inference network is also designed for enabling inductive analysis. A gating mechanism is further introduced to dynamically tune the Gaussian mixture distributions. Extensive experimental results on a variety of real-life datasets demonstrate the effectiveness of our method.

This work aims to implement Long Short-Term Memory mixture density networks (LSTM-MDNs) for Value-at-Risk forecasting and compare their performance with established models (historical simulation, CMM, and GARCH) using a defined backtesting procedure. The focus was on the neural network's ability to capture volatility clustering and its real-world applicability. Three architectures were tested: a 2-component mixture density network, a regularized 2-component model (Arimond et al., 2020), and a 3-component mixture model, the latter being tested for the first time in Value-at-Risk forecasting. Backtesting was performed on three stock indices (FTSE 100, S&P 500, EURO STOXX 50) over two distinct two-year periods (2017-2018 as a calm period, 2021-2022 as turbulent). Model performance was assessed through unconditional coverage and independence assumption tests. The neural network's ability to handle volatility clustering was validated via correlation analysis and graphical evaluation. Results show limited success for the neural network approach. LSTM-MDNs performed poorly for 2017/2018 but outperformed benchmark models in 2021/2022. The LSTM mechanism allowed the neural network to capture volatility clustering similarly to GARCH models. However, several issues were identified: the need for proper model initialization and reliance on large datasets for effective learning. The findings suggest that while LSTM-MDNs provide adequate risk forecasts, further research and adjustments are necessary for stable performance.

In recent years, transformer-based models have gained prominence in multivariate long-term time series forecasting (LTSF), demonstrating significant advancements despite facing challenges such as high computational demands, difficulty in capturing temporal dynamics, and managing long-term dependencies. The emergence of LTSF-Linear, with its straightforward linear architecture, has notably outperformed transformer-based counterparts, prompting a reevaluation of the transformer's utility in time series forecasting. In response, this paper presents an adaptation of a recent architecture termed extended LSTM (xLSTM) for LTSF. xLSTM incorporates exponential gating and a revised memory structure with higher capacity that has good potential for LTSF. Our adopted architecture for LTSF termed as xLSTMTime surpasses current approaches. We compare xLSTMTime's performance against various state-of-the-art models across multiple real-world da-tasets, demonstrating superior forecasting capabilities. Our findings suggest that refined recurrent architectures can offer competitive alternatives to transformer-based models in LTSF tasks, po-tentially redefining the landscape of time series forecasting.

We introduce AutoGluon-TimeSeries - an open-source AutoML library for probabilistic time series forecasting. Focused on ease of use and robustness, AutoGluon-TimeSeries enables users to generate accurate point and quantile forecasts with just 3 lines of Python code. Built on the design philosophy of AutoGluon, AutoGluon-TimeSeries leverages ensembles of diverse forecasting models to deliver high accuracy within a short training time. AutoGluon-TimeSeries combines both conventional statistical models, machine-learning based forecasting approaches, and ensembling techniques. In our evaluation on 29 benchmark datasets, AutoGluon-TimeSeries demonstrates strong empirical performance, outperforming a range of forecasting methods in terms of both point and quantile forecast accuracy, and often even improving upon the best-in-hindsight combination of prior methods.

The cryptocurrency market is highly volatile compared to traditional financial markets. Hence, forecasting its volatility is crucial for risk management. In this paper, we investigate CryptoQuant data (e.g. on-chain analytics, exchange and miner data) and whale-alert tweets, and explore their relationship to Bitcoin's next-day volatility, with a focus on extreme volatility spikes. We propose a deep learning Synthesizer Transformer model for forecasting volatility. Our results show that the model outperforms existing state-of-the-art models when forecasting extreme volatility spikes for Bitcoin using CryptoQuant data as well as whale-alert tweets. We analysed our model with the Captum XAI library to investigate which features are most important. We also backtested our prediction results with different baseline trading strategies and the results show that we are able to minimize drawdown while keeping steady profits. Our findings underscore that the proposed method is a useful tool for forecasting extreme volatility movements in the Bitcoin market.

Weather forecasting is a fundamental problem for anticipating and mitigating the impacts of climate change. Recently, data-driven approaches for weather forecasting based on deep learning have shown great promise, achieving accuracies that are competitive with operational systems. However, those methods often employ complex, customized architectures without sufficient ablation analysis, making it difficult to understand what truly contributes to their success. Here we introduce Stormer, a simple transformer model that achieves state-of-the-art performance on weather forecasting with minimal changes to the standard transformer backbone. We identify the key components of Stormer through careful empirical analyses, including weather-specific embedding, randomized dynamics forecast, and pressure-weighted loss. At the core of Stormer is a randomized forecasting objective that trains the model to forecast the weather dynamics over varying time intervals. During inference, this allows us to produce multiple forecasts for a target lead time and combine them to obtain better forecast accuracy. On WeatherBench 2, Stormer performs competitively at short to medium-range forecasts and outperforms current methods beyond 7 days, while requiring orders-of-magnitude less training data and compute. Additionally, we demonstrate Stormer's favorable scaling properties, showing consistent improvements in forecast accuracy with increases in model size and training tokens. Code and checkpoints are available at https://github.com/tung-nd/stormer.

In traditional quantitative trading practice, navigating the complicated and dynamic financial market presents a persistent challenge. Fully capturing various market variables, including long-term information, as well as essential signals that may lead to profit remains a difficult task for learning algorithms. In order to tackle this challenge, this paper introduces quantformer, an enhanced neural network architecture based on transformers, to build investment factors. By transfer learning from sentiment analysis, quantformer not only exploits its original inherent advantages in capturing long-range dependencies and modeling complex data relationships, but is also able to solve tasks with numerical inputs and accurately forecast future returns over a given period. This work collects more than 5,000,000 rolling data of 4,601 stocks in the Chinese capital market from 2010 to 2019. The results of this study demonstrated the model's superior performance in predicting stock trends compared with other 100 factor-based quantitative strategies. Notably, the model's innovative use of transformer-liked model to establish factors, in conjunction with market sentiment information, has been shown to enhance the accuracy of trading signals significantly, thereby offering promising implications for the future of quantitative trading strategies.

In recent years, generative pre-trained paradigms such as Large Language Models (LLMs) and Large Vision Models (LVMs) have achieved revolutionary advancements and widespread real-world applications. Particularly, the emergence of pre-trained LLMs-based temporal works, compared to previous deep model approaches, has demonstrated superior generalization and robustness, showcasing the potential of generative pre-trained paradigms as foundation models for time series. However, those LLMs-based works mainly focus on cross-modal research, i.e., leveraging the language capabilities of LLMs in time series contexts. Although they have achieved impressive performance, there still exist the issues of concept drift caused by differences in data distribution and inflexibility caused by misalignment of dimensions. To this end, inspired by recent work on LVMs, we reconsider the paradigm of time series modeling. In this paper, we comprehensively explore, for the first time, the effectiveness and superiority of the Generative Pre-trained Diffusion (GPD) paradigm in real-world multivariate time series forecasting (TSF). Specifically, to mitigate performance bias introduced by sophisticated networks, we propose a straightforward MLP diffusion network for unconditional modeling of time series. Then we employ a zero-shot and tuning-free method to predict (generate) future data using historical data as prompts. The GPD paradigm is established on the time series modality, effectively preventing the phenomenon of concept drift, and enabling flexible forecasting of arbitrary lengths. We demonstrate that the GPD paradigm achieves comprehensive performance and generalization comparable to current SOTA LLM-based and deep model paradigms on mainstream benchmarks and various TSF tasks. Extensive experiments validate the potential of the GPD paradigm and its assistance in future related research.

Our research aims to find the best model that uses companies projections and sector performances and how the given company fares accordingly to correctly predict equity share prices for both short and long term goals.

Recently, channel-independent methods have achieved state-of-the-art performance in multivariate time series (MTS) forecasting. Despite reducing overfitting risks, these methods miss potential opportunities in utilizing channel dependence for accurate predictions. We argue that there exist locally stationary lead-lag relationships between variates, i.e., some lagged variates may follow the leading indicators within a short time period. Exploiting such channel dependence is beneficial since leading indicators offer advance information that can be used to reduce the forecasting difficulty of the lagged variates. In this paper, we propose a new method named LIFT that first efficiently estimates leading indicators and their leading steps at each time step and then judiciously allows the lagged variates to utilize the advance information from leading indicators. LIFT plays as a plugin that can be seamlessly collaborated with arbitrary time series forecasting methods. Extensive experiments on six real-world datasets demonstrate that LIFT improves the state-of-the-art methods by 5.5% in average forecasting performance. Our code is available at https://github.com/SJTU-Quant/LIFT.

To reject the Efficient Market Hypothesis a set of 5 technical indicators and 23 fundamental indicators was identified to establish the possibility of generating excess returns on the stock market. Leveraging these data points and various classification machine learning models, trading data of the 505 equities on the US S&P500 over the past 20 years was analysed to develop a classifier effective for our cause. From any given day, we were able to predict the direction of change in price by 1% up to 10 days in the future. The predictions had an overall accuracy of 83.62% with a precision of 85% for buy signals and a recall of 100% for sell signals. Moreover, we grouped equities by their sector and repeated the experiment to see if grouping similar assets together positively effected the results but concluded that it showed no significant improvements in the performance rejecting the idea of sector-based analysis. Also, using feature ranking we could identify an even smaller set of 6 indicators while maintaining similar accuracies as that from the original 28 features and also uncovered the importance of buy, hold and sell analyst ratings as they came out to be the top contributors in the model. Finally, to evaluate the effectiveness of the classifier in real-life situations, it was backtested on FAANG equities using a modest trading strategy where it generated high returns of above 60% over the term of the testing dataset. In conclusion, our proposed methodology with the combination of purposefully picked features shows an improvement over the previous studies, and our model predicts the direction of 1% price changes on the 10th day with high confidence and with enough buffer to even build a robotic trading system.

Real-world time series often exhibit a non-stationary nature, degrading the performance of pre-trained forecasting models. Test-Time Adaptation (TTA) addresses this by adjusting models during inference, but existing methods typically update the full model, increasing memory and compute costs. We propose PETSA, a parameter-efficient method that adapts forecasters at test time by only updating small calibration modules on the input and output. PETSA uses low-rank adapters and dynamic gating to adjust representations without retraining. To maintain accuracy despite limited adaptation capacity, we introduce a specialized loss combining three components: (1) a robust term, (2) a frequency-domain term to preserve periodicity, and (3) a patch-wise structural term for structural alignment. PETSA improves the adaptability of various forecasting backbones while requiring fewer parameters than baselines. Experimental results on benchmark datasets show that PETSA achieves competitive or better performance across all horizons. Our code is available at: https://github.com/BorealisAI/PETSA

Volatility clustering is an important characteristic that has a significant effect on the behavior of stock markets. However, designing robust models for accurate prediction of future volatilities of stock prices is a very challenging research problem. We present several volatility models based on generalized autoregressive conditional heteroscedasticity (GARCH) framework for modeling the volatility of ten stocks listed in the national stock exchange (NSE) of India. The stocks are selected from the auto sector and the banking sector of the Indian economy, and they have a significant impact on the sectoral index of their respective sectors in the NSE. The historical stock price records from Jan 1, 2010, to Apr 30, 2021, are scraped from the Yahoo Finance website using the DataReader API of the Pandas module in the Python programming language. The GARCH modules are built and fine-tuned on the training data and then tested on the out-of-sample data to evaluate the performance of the models. The analysis of the results shows that asymmetric GARCH models yield more accurate forecasts on the future volatility of stocks.

Pre-trained Large Language Models (LLMs) encapsulate large amounts of knowledge and take enormous amounts of compute to train. We make use of this resource, together with the observation that LLMs are able to transfer knowledge and performance from one domain or even modality to another seemingly-unrelated area, to help with multivariate demand time series forecasting. Attention in transformer-based methods requires something worth attending to -- more than just samples of a time-series. We explore different methods to map multivariate input time series into the LLM token embedding space. In particular, our novel multivariate patching strategy to embed time series features into decoder-only pre-trained Transformers produces results competitive with state-of-the-art time series forecasting models. We also use recently-developed weight-based diagnostics to validate our findings.

The success of large pretrained models in natural language processing (NLP) and computer vision (CV) has opened new avenues for constructing foundation models for time series forecasting (TSF). Traditional TSF foundation models rely heavily on numerical data fitting. In contrast, the human brain is inherently skilled at processing visual information, prefer predicting future trends by observing visualized sequences. From a biomimetic perspective, utilizing models to directly process numerical sequences might not be the most effective route to achieving Artificial General Intelligence (AGI). This paper proposes ViTime, a novel Visual Intelligence-based foundation model for TSF. ViTime overcomes the limitations of numerical time series data fitting by utilizing visual data processing paradigms and employs a innovative data synthesis method during training, called Real Time Series (RealTS). Experiments on a diverse set of previously unseen forecasting datasets demonstrate that ViTime achieves state-of-the-art zero-shot performance, even surpassing the best individually trained supervised models in some situations. These findings suggest that visual intelligence can significantly enhance time series analysis and forecasting, paving the way for more advanced and versatile models in the field. The code for our framework is accessible at https://github.com/IkeYang/ViTime.

Stock price prediction is a challenging task and a lot of propositions exist in the literature in this area. Portfolio construction is a process of choosing a group of stocks and investing in them optimally to maximize the return while minimizing the risk. Since the time when Markowitz proposed the Modern Portfolio Theory, several advancements have happened in the area of building efficient portfolios. An investor can get the best benefit out of the stock market if the investor invests in an efficient portfolio and could take the buy or sell decision in advance, by estimating the future asset value of the portfolio with a high level of precision. In this project, we have built an efficient portfolio and to predict the future asset value by means of individual stock price prediction of the stocks in the portfolio. As part of building an efficient portfolio we have studied multiple portfolio optimization methods beginning with the Modern Portfolio theory. We have built the minimum variance portfolio and optimal risk portfolio for all the five chosen sectors by using past daily stock prices over the past five years as the training data, and have also conducted back testing to check the performance of the portfolio. A comparative study of minimum variance portfolio and optimal risk portfolio with equal weight portfolio is done by backtesting.

Stock movement prediction, a fundamental task in financial time-series forecasting, requires identifying and retrieving critical influencing factors from vast amounts of time-series data. However, existing text-trained or numeric similarity-based retrieval methods fall short in handling complex financial analysis. To address this, we propose the first retrieval-augmented generation (RAG) framework for financial time-series forecasting, featuring three key innovations: a fine-tuned 1B parameter large language model (StockLLM) as the backbone, a novel candidate selection method leveraging LLM feedback, and a training objective that maximizes similarity between queries and historically significant sequences. This enables our retriever, FinSeer, to uncover meaningful patterns while minimizing noise in complex financial data. We also construct new datasets integrating financial indicators and historical stock prices to train FinSeer and ensure robust evaluation. Experimental results demonstrate that our RAG framework outperforms bare StockLLM and random retrieval, highlighting its effectiveness, while FinSeer surpasses existing retrieval methods, achieving an 8\% higher accuracy on BIGDATA22 and retrieving more impactful sequences. This work underscores the importance of tailored retrieval models in financial forecasting and provides a novel framework for future research.

We introduce Sundial, a family of native, flexible, and scalable time series foundation models. To predict the next-patch's distribution, we propose a TimeFlow Loss based on flow-matching, which facilitates native pre-training of Transformers on time series without discrete tokenization. Conditioned on arbitrary-length time series, our model is pre-trained without specifying any prior distribution and can generate multiple probable predictions, achieving flexibility in representation learning beyond using parametric densities. Towards time series foundation models, we leverage minimal but crucial adaptations of Transformers and curate TimeBench with 1 trillion time points, comprising mostly real-world datasets and synthetic data. By mitigating mode collapse through TimeFlow Loss, we pre-train a family of Sundial models on TimeBench, which exhibit unprecedented model capacity and generalization performance on zero-shot forecasting. In addition to presenting good scaling behavior, Sundial achieves new state-of-the-art on both point forecasting and probabilistic forecasting benchmarks. We believe that Sundial's pioneering generative paradigm will facilitate a wide variety of forecasting scenarios.

In light of recent work on scheduling with predicted job sizes, we consider the effect of the cost of predictions in queueing systems, removing the assumption in prior research that predictions are external to the system's resources and/or cost-free. In particular, we introduce a novel approach to utilizing predictions, SkipPredict, designed to address their inherent cost. Rather than uniformly applying predictions to all jobs, we propose a tailored approach that categorizes jobs based on their prediction requirements. To achieve this, we employ one-bit "cheap predictions" to classify jobs as either short or long. SkipPredict prioritizes predicted short jobs over long jobs, and for the latter, SkipPredict applies a second round of more detailed "expensive predictions" to approximate Shortest Remaining Processing Time for these jobs. Our analysis takes into account the cost of prediction. We examine the effect of this cost for two distinct models. In the external cost model, predictions are generated by some external method without impacting job service times but incur a cost. In the server time cost model, predictions themselves require server processing time, and are scheduled on the same server as the jobs.

The stock market is a network which provides a platform for almost all major economic transactions. While investing in the stock market is a good idea, investing in individual stocks may not be, especially for the casual investor. Smart stock-picking requires in-depth research and plenty of dedication. Predicting this stock value offers enormous arbitrage profit opportunities. This attractiveness of finding a solution has prompted researchers to find a way past problems like volatility, seasonality, and dependence on time. This paper surveys recent literature in the domain of natural language processing and machine learning techniques used to predict stock market movements. The main contributions of this paper include the sophisticated categorizations of many recent articles and the illustration of the recent trends of research in stock market prediction and its related areas.

Price responsiveness is a major feature of end use customers (EUCs) that participate in demand response (DR) programs, and has been conventionally modeled with static demand functions, which take the electricity price as the input and the aggregate energy consumption as the output. This, however, neglects the inherent temporal correlation of the EUC behaviors, and may result in large errors when predicting the actual responses of EUCs in real-time pricing (RTP) programs. In this paper, we propose a dynamical DR model so as to capture the temporal behavior of the EUCs. The states in the proposed dynamical DR model can be explicitly chosen, in which case the model can be represented by a linear function or a multi-layer feedforward neural network, or implicitly chosen, in which case the model can be represented by a recurrent neural network or a long short-term memory unit network. In both cases, the dynamical DR model can be learned from historical price and energy consumption data. Numerical simulation illustrated how the states are chosen and also showed the proposed dynamical DR model significantly outperforms the static ones.

This study examines the effects of de-globalization trends on international trade networks and their role in improving forecasts for economic growth. Using section-level trade data from nearly 200 countries from 2010 to 2022, we identify significant shifts in the network topology driven by rising trade policy uncertainty. Our analysis highlights key global players through centrality rankings, with the United States, China, and Germany maintaining consistent dominance. Using a horse race of supervised regressors, we find that network topology descriptors evaluated from section-specific trade networks substantially enhance the quality of a country's GDP growth forecast. We also find that non-linear models, such as Random Forest, XGBoost, and LightGBM, outperform traditional linear models used in the economics literature. Using SHAP values to interpret these non-linear model's predictions, we find that about half of most important features originate from the network descriptors, underscoring their vital role in refining forecasts. Moreover, this study emphasizes the significance of recent economic performance, population growth, and the primary sector's influence in shaping economic growth predictions, offering novel insights into the intricacies of economic growth forecasting.

Developing an accurate tourism forecasting model is essential for making desirable policy decisions for tourism management. Early studies on tourism management focus on discovering external factors related to tourism demand. Recent studies utilize deep learning in demand forecasting along with these external factors. They mainly use recursive neural network models such as LSTM and RNN for their frameworks. However, these models are not suitable for use in forecasting tourism demand. This is because tourism demand is strongly affected by changes in various external factors, and recursive neural network models have limitations in handling these multivariate inputs. We propose a multi-head attention CNN model (MHAC) for addressing these limitations. The MHAC uses 1D-convolutional neural network to analyze temporal patterns and the attention mechanism to reflect correlations between input variables. This model makes it possible to extract spatiotemporal characteristics from time-series data of various variables. We apply our forecasting framework to predict inbound tourist changes in South Korea by considering external factors such as politics, disease, season, and attraction of Korean culture. The performance results of extensive experiments show that our method outperforms other deep-learning-based prediction frameworks in South Korea tourism forecasting.

Oil production forecasting is an important step in controlling the cost-effect and monitoring the functioning of petroleum reservoirs. As a result, oil production forecasting makes it easier for reservoir engineers to develop feasible projects, which helps to avoid risky investments and achieve long-term growth. As a result, reliable petroleum reservoir forecasting is critical for controlling and managing the effective cost of oil reservoirs. Oil production is influenced by reservoir qualities such as porosity, permeability, compressibility, fluid saturation, and other well operational parameters. Three-time series algorithms i.e., Seasonal Naive method, Exponential Smoothening and ARIMA to forecast the Distillate Fuel Oil Refinery and Propane Blender net production for the next two years.

Pre-trained foundation models (FMs) have shown exceptional performance in univariate time series forecasting tasks. However, several practical challenges persist, including managing intricate dependencies among features and quantifying uncertainty in predictions. This study aims to tackle these critical limitations by introducing adapters; feature-space transformations that facilitate the effective use of pre-trained univariate time series FMs for multivariate tasks. Adapters operate by projecting multivariate inputs into a suitable latent space and applying the FM independently to each dimension. Inspired by the literature on representation learning and partially stochastic Bayesian neural networks, we present a range of adapters and optimization/inference strategies. Experiments conducted on both synthetic and real-world datasets confirm the efficacy of adapters, demonstrating substantial enhancements in forecasting accuracy and uncertainty quantification compared to baseline methods. Our framework, AdaPTS, positions adapters as a modular, scalable, and effective solution for leveraging time series FMs in multivariate contexts, thereby promoting their wider adoption in real-world applications. We release the code at https://github.com/abenechehab/AdaPTS.

We present a joint forecasting framework for time series prediction that contrasts with traditional direct or recursive methods. This framework achieves state-of-the-art performance for our designed foundation model, YingLong, and reveals a novel scaling effect: longer outputs significantly enhance model accuracy due to delayed chain-of-thought reasoning in our non-causal approach. YingLong is a non-causal, bidirectional attention encoder-only transformer trained through masked token recovery, aligning more effectively with language understanding tasks than with generation tasks. Additionally, we boost performance by tackling output variance with a multi-input ensemble. We release four foundation models ranging from 6M to 300M parameters, demonstrating superior results in zero-shot tasks on the ETT and Weather datasets. YingLong achieves more than 60% best performance. To ensure generalizability, we assessed the models using the GIFT-Eval benchmark, which comprises 23 time series datasets across 7 domains. Yinglong significantly outperformed the best time-series foundation models, end-to-end trained models by 14% and 44% in rank respectively.The pretrained 300M model is available at https://huggingface.co/qcw1314/YingLong_300m

We propose an efficient design of Transformer-based models for multivariate time series forecasting and self-supervised representation learning. It is based on two key components: (i) segmentation of time series into subseries-level patches which are served as input tokens to Transformer; (ii) channel-independence where each channel contains a single univariate time series that shares the same embedding and Transformer weights across all the series. Patching design naturally has three-fold benefit: local semantic information is retained in the embedding; computation and memory usage of the attention maps are quadratically reduced given the same look-back window; and the model can attend longer history. Our channel-independent patch time series Transformer (PatchTST) can improve the long-term forecasting accuracy significantly when compared with that of SOTA Transformer-based models. We also apply our model to self-supervised pre-training tasks and attain excellent fine-tuning performance, which outperforms supervised training on large datasets. Transferring of masked pre-trained representation on one dataset to others also produces SOTA forecasting accuracy. Code is available at: https://github.com/yuqinie98/PatchTST.