B.4 Existing theoretical intuition and empirical comparison to the proposed OCP block.

Code is available at this repository: https://github.com/thuml/Koopa.

We study U.S. Treasury yield curve forecasting under distributional uncertainty and recast forecasting as an operations research and managerial decision problem. Rather than minimizing average forecast error, the forecaster selects a decision rule that minimizes worst case expected loss over an ambiguity set of forecast error distributions. To this end, we propose a distributionally robust ensemble forecasting framework that integrates parametric factor models with high dimensional nonparametric machine learning models through adaptive forecast combinations. The framework consists of three machine learning components. First, a rolling window Factor Augmented Dynamic Nelson Siegel model captures level, slope, and curvature dynamics using principal components extracted from economic indicators. Second, Random Forest models capture nonlinear interactions among macro financial drivers and lagged Treasury yields. Third, distributionally robust forecast combination schemes aggregate heterogeneous forecasts under moment uncertainty, penalizing downside tail risk via expected shortfall and stabilizing second moment estimation through ridge regularized covariance matrices. The severity of the worst case criterion is adjustable, allowing the forecaster to regulate the trade off between robustness and statistical efficiency. Using monthly data, we evaluate out of sample forecasts across maturities and horizons from one to twelve months ahead. Adaptive combinations deliver superior performance at short horizons, while Random Forest forecasts dominate at longer horizons. Extensions to global sovereign bond yields confirm the stability and generalizability of the proposed framework.

The ionosphere is a critical component of near-Earth space, shaping GNSS accuracy, high-frequency communications, and aviation operations. For these reasons, accurate forecasting and modeling of ionospheric variability has become increasingly relevant. To address this gap, we present IonCast, a suite of deep learning models that include a GraphCast-inspired model tailored for ionospheric dynamics. IonCast leverages spatiotemporal learning to forecast global Total Electron Content (TEC), integrating diverse physical drivers and observational datasets. Validating on held-out storm-time and quiet conditions highlights improved skill compared to persistence. By unifying heterogeneous data with scalable graph-based spatiotemporal learning, IonCast demonstrates how machine learning can augment physical understanding of ionospheric variability and advance operational space weather resilience.

This paper introduces a classification method using in-context learning in time-series foundation models (TSFM). We show how data, which was not part of the TSFM training data corpus, can be classified without the need of finetuning the model. Examples are represented in the form of targets (class id) and covariates (data matrix) within the prompt of the model, which enables to classify an unknown covariate data pattern alongside the forecast axis through in-context learning. We apply this method to vibration data for assessing the health state of a bearing within a servo-press motor. The method transforms frequency domain reference signals into pseudo time-series patterns, generates aligned covariate and target signals, and uses the TSFM to predict probabilities how classified data corresponds to predefined labels. Leveraging the scalability of pre-trained models this method demonstrates efficacy across varied operational conditions.

Pre-trained Time Series Foundational Models (TSFMs) represent a significant advance, capable of forecasting diverse time series with complex characteristics, including varied seasonalities, trends, and long-range dependencies. Despite their primary goal of universal time series forecasting, their efficacy is far from uniform; divergent training protocols and data sources cause individual TSFMs to exhibit highly variable performance across different forecasting tasks, domains, and horizons. Leveraging this complementary expertise by arbitrating existing TSFM outputs presents a compelling strategy, yet this remains a largely unexplored area of research. In this paper, we conduct a thorough examination of how different TSFMs exhibit specialized performance profiles across various forecasting settings, and how we can effectively leverage this behavior in arbitration between different time series models. We specifically analyze how factors such as model selection and forecast horizon distribution can influence the efficacy of arbitration strategies. Based on this analysis, we propose Synapse, a novel arbitration framework for TSFMs. Synapse is designed to dynamically leverage a pool of TSFMs, assign and adjust predictive weights based on their relative, context-dependent performance, and construct a robust forecast distribution by adaptively sampling from the output quantiles of constituent models. Experimental results demonstrate that Synapse consistently outperforms other popular ensembling techniques as well as individual TSFMs, demonstrating Synapse's efficacy in time series forecasting.

This paper presents a methodological approach to financial time series analysis by combining causal discovery and uncertainty-aware forecasting. As a case study, we focus on four key U.S. macroeconomic indicators -- GDP, economic growth, inflation, and unemployment -- and we apply the LPCMCI framework with Gaussian Process Distance Correlation (GPDC) to uncover dynamic causal relationships in quarterly data from 1970 to 2021. Our results reveal a robust unidirectional causal link from economic growth to GDP and highlight the limited connectivity of inflation, suggesting the influence of latent factors. Unemployment exhibits strong autore-gressive dependence, motivating its use as a case study for probabilistic forecasting. Leveraging the Chronos framework, a large language model trained for time series, we perform zero-shot predictions on unemployment. This approach delivers accurate forecasts one and two quarters ahead, without requiring task-specific training. Crucially, the model's uncertainty-aware predictions yield 90% confidence intervals, enabling effective anomaly detection through statistically principled deviation analysis. This study demonstrates the value of combining causal structure learning with probabilistic language models to inform economic policy and enhance forecasting robustness.

Neural activity forecasting is central to understanding neural systems and enabling closed-loop control. While deep learning has recently advanced the state-of-the-art in the time series forecasting literature, its application to neural activity forecasting remains limited. To bridge this gap, we systematically evaluated eight probabilistic deep learning models, including two foundation models, that have demonstrated strong performance on general forecasting benchmarks. We compared them against four classical statistical models and two baseline methods on spontaneous neural activity recorded from mouse cortex via widefield imaging. Across prediction horizons, several deep learning models consistently outperformed classical approaches, with the best model producing informative forecasts up to 1.5 seconds into the future. Our findings point toward future control applications and open new avenues for probing the intrinsic temporal structure of neural activity.

The lack of standardization in seizure forecasting slows progress in the field and limits the clinical translation of forecasting models. In this work, we introduce a Python-based framework aimed at streamlining the development, assessment, and documentation of individualized seizure forecasting algorithms. The framework automates data labeling, cross-validation splitting, forecast post-processing, performance evaluation, and reporting. It supports various forecasting horizons and includes a model card that documents implementation details, training and evaluation settings, and performance metrics. Three different models were implemented as a proof-of-concept. The models leveraged features extracted from time series data and seizure periodicity. Model performance was assessed using time series cross-validation and key deterministic and probabilistic metrics. Implementation of the three models was successful, demonstrating the flexibility of the framework. The results also emphasize the importance of careful model interpretation due to variations in probability scaling, calibration, and subject-specific differences. Although formal usability metrics were not recorded, empirical observations suggest reduced development time and methodological consistency, minimizing unintentional variations that could affect the comparability of different approaches. As a proof-of-concept, this validation is inherently limited, relying on a single-user experiment without statistical analyses or replication across independent datasets. At this stage, our objective is to make the framework publicly available to foster community engagement, facilitate experimentation, and gather feedback. In the long term, we aim to contribute to the establishment of a consensus on a standardized methodology for the development and validation of seizure forecasting algorithms in people with epilepsy.

Forecasting stock prices remains challenging due to the volatile and non-linear nature of financial markets. Despite the promise of deep learning, issues such as mode collapse, unstable training, and difficulty in capturing temporal and feature level correlations have limited the applications of GANs in this domain. We propose a GRU-based Encoder-Decoder GAN (EDGAN) model that strikes a balance between expressive power and simplicity. The model introduces key innovations such as a temporal decoder with residual connections for precise reconstruction, conditioning on static and dynamic covariates for contextual learning, and a windowing mechanism to capture temporal dynamics. Here, the generator uses a dense encoder-decoder framework with residual GRU blocks. Extensive experiments on diverse stock datasets demonstrate that EDGAN achieves superior forecasting accuracy and training stability, even in volatile markets. It consistently outperforms traditional GAN variants in forecasting accuracy and convergence stability under market conditions.