Spatio-temporal process models are often used for modeling dynamic physical and biological phenomena that evolve across space and time. These phenomena may exhibit environmental heterogeneity and complex interactions that are difficult to capture using traditional statistical process models such as Gaussian processes. This work proposes the use of Fourier neural operators (FNOs) for constructing statistical dynamical spatio-temporal models for forecasting. An FNO is a flexible mapping of functions that approximates the solution operator of possibly unknown linear or non-linear partial differential equations (PDEs) in a computationally efficient manner. It does so using samples of inputs and their respective outputs, and hence explicit knowledge of the underlying PDE is not required. Through simulations from a nonlinear PDE with known solution, we compare FNO forecasts to those from state-of-the-art statistical spatio-temporal-forecasting methods. Further, using sea surface temperature data over the Atlantic Ocean and precipitation data across Europe, we demonstrate the ability of FNO-based dynamic spatio-temporal (DST) statistical modeling to capture complex real-world spatio-temporal dependencies. Using collections of testing instances, we show that the FNO-DST forecasts are accurate with valid uncertainty quantification.

Financial time series forecasting is central to trading, portfolio optimization, and risk management, yet it remains challenging due to noisy, non-stationary, and heterogeneous data. Recent advances in time series foundation models (TSFMs), inspired by large language models, offer a new paradigm for learning generalizable temporal representations from large and diverse datasets. This paper presents the first comprehensive empirical study of TSFMs in global financial markets. Using a large-scale dataset of daily excess returns across diverse markets, we evaluate zero-shot inference, fine-tuning, and pre-training from scratch against strong benchmark models. We find that off-the-shelf pre-trained TSFMs perform poorly in zero-shot and fine-tuning settings, whereas models pre-trained from scratch on financial data achieve substantial forecasting and economic improvements, underscoring the value of domain-specific adaptation. Increasing the dataset size, incorporating synthetic data augmentation, and applying hyperparameter tuning further enhance performance.

This technical report describes the AIA Forecaster, a Large Language Model (LLM)-based system for judgmental forecasting using unstructured data. The AIA Forecaster approach combines three core elements: agentic search over high-quality news sources, a supervisor agent that reconciles disparate forecasts for the same event, and a set of statistical calibration techniques to counter behavioral biases in large language models. On the ForecastBench benchmark (Karger et al., 2024), the AIA Forecaster achieves performance equal to human superforecasters, surpassing prior LLM baselines. In addition to reporting on ForecastBench, we also introduce a more challenging forecasting benchmark sourced from liquid prediction markets. While the AIA Forecaster underperforms market consensus on this benchmark, an ensemble combining AIA Forecaster with market consensus outperforms consensus alone, demonstrating that our forecaster provides additive information. Our work establishes a new state of the art in AI forecasting and provides practical, transferable recommendations for future research. To the best of our knowledge, this is the first work that verifiably achieves expert-level forecasting at scale.

We introduce M2VN: Multi-Modal Volatility Network, a novel deep learning-based framework for financial volatility forecasting that unifies time series features with unstructured news data. M2VN leverages the representational power of deep neural networks to address two key challenges in this domain: (i) aligning and fusing heterogeneous data modalities, numerical financial data and textual information, and (ii) mitigating look-ahead bias that can undermine the validity of financial models. To achieve this, M2VN combines open-source market features with news embeddings generated by Time Machine GPT, a recently introduced point-in-time LLM, ensuring temporal integrity. An auxiliary alignment loss is introduced to enhance the integration of structured and unstructured data within the deep learning architecture. Extensive experiments demonstrate that M2VN consistently outperforms existing baselines, underscoring its practical value for risk management and financial decision-making in dynamic markets.

Small Earth data are geoscience observations with limited short-term monitoring variability, providing sparse but meaningful measurements, typically exhibiting spatiotemporal correlations. Spatiotemporal forecasting on such data is crucial for understanding geoscientific processes despite their small scale. However, conventional deep learning models for spatiotemporal forecasting requires task-specific training for different scenarios. Foundation models do not need task-specific training, but they often exhibit forecasting bias toward the global mean of the pretraining distribution. Here we propose a simple and robust approach for spatiotemporally correlated small Earth data forecasting. The essential idea is to characterize and quantify spatiotemporal patterns of small Earth data and then utilize tabular foundation models for accurate forecasting across different scenarios. Comparative results across three typical scenarios demonstrate that our forecasting approach achieves superior accuracy compared to the graph deep learning model (T -GCN) and tabular foundation model (TabPFN) in the majority of instances, exhibiting stronger robustness. Keywords: Small Earth data, Spatiotemporal correlations, Tabular foundation model, Forecasting, Deep learning 1. Introduction Small Earth data refers to geoscience time-series observations in which short-term monitoring provides limited informative variation, resulting in only sparse but meaningful measurements being available. These data predominantly possess spatiotemporal correlations. Despite their small scale, forecasting on such data is of critical importance for understanding geoscientific processes (Saad et al., 2024; Y u et al., 2024).

Time series forecasting has attracted significant attention in recent decades.

Deep time series forecasting has emerged as a booming direction in recent years. Despite the exponential growth of community interests, researchers are sometimes confused about the direction of their efforts due to minor improvements on standard benchmarks. In this paper, we notice that, unlike image recognition, whose well-acknowledged and realizable goal is 100% accuracy, time series forecasting inherently faces a non-zero error lower bound due to its partially observable and uncertain nature. To pinpoint the research objective and release researchers from saturated tasks, this paper focuses on a fundamental question: how to estimate the performance upper bound of deep time series forecasting? Going beyond classical series-wise predictability metrics, e.g., ADF test, we realize that the forecasting performance is highly related to window-wise properties because of the sequence-to-sequence forecasting paradigm of deep time series models. Based on rigorous statistical tests of over 2,800 newly trained deep forecasters, we discover a significant exponential relationship between the minimum forecasting error of deep models and the complexity of window-wise series patterns, which is termed the accuracy law. The proposed accuracy law successfully guides us to identify saturated tasks from widely used benchmarks and derives an effective training strategy for large time series models, offering valuable insights for future research. Despite these advancements, we notice that the latest proposed models have shown minor improvements on existing widely used benchmarks. As presented in Figure 1, the improvement in the performance of deep time series models on four standard benchmarks has slowed significantly over the past three years. For instance, on the ETT benchmark (Zhou et al., 2021), the relative forecasting performance improvements exhibited a continuous downward trend from 2022 to 2025, with values of 14.98%, 7.77%, 3.93%, and 3.51% respectively.