block bootstrap

This work addresses the challenge of forecasting irregularly sampled multivariate time series (IMTS), where existing approaches often rely on resampling that disrupts the intrinsic sampling patterns encoded in the original timestamps, thereby degrading predictive performance. To overcome this limitation, the authors propose ReIMTS, a novel framework that eschews resampling entirely. Instead, it recursively partitions the input into variable-length subsequences to preserve the native temporal structure and introduces an irregularity-aware representation fusion mechanism that jointly captures multiscale temporal dependencies—from global to local—and inter-variable relationships. Extensive experiments on multiple real-world datasets demonstrate that ReIMTS achieves an average improvement of 27.1% in forecasting accuracy, significantly outperforming current state-of-the-art methods.

The sampling distribution of spatial spectral averages is analytically intractable, and existing frequency-domain bootstrap methods apply only to restrictive cases—such as Gaussian processes—limiting uncertainty quantification for general spatial data. To address this, we propose a hybrid resampling framework that integrates spatial subsampling with frequency-domain bootstrapping: subsampling captures the asymptotic variance of spectral averages, while bootstrapping models the shape of the sampling distribution; their synergy overcomes traditional limitations on process assumptions and statistic forms. Under mild spatial dependence, our method robustly approximates the sampling distributions of broad classes of spatial spectral statistics—including periodogram averages—enabling nonparametric, universally applicable uncertainty estimation. Experiments on remote sensing and meteorological gridded data demonstrate substantial improvements in both applicability and reliability of frequency-domain inference.

This work proposes an interactive visual analytics approach to address the challenges of visual clutter and redundancy in large-scale time series visualization, which often obscure critical trends. By integrating M4 sampling, dynamic time warping (DTW) similarity computation, and a greedy selection strategy, the method automatically identifies a representative subset of time series that preserves essential patterns while minimizing redundancy. A coordinated multi-view visualization framework further enables users to efficiently explore and interpret the data. The proposed technique significantly enhances visual clarity, interpretability, and analytical efficiency without sacrificing the core temporal characteristics of the original dataset.

Existing time series chain methods are confined to individual sequences and struggle to capture anomalous evolution patterns across interruptions or related sequences. This work proposes a novel formulation—Joint Time Series Chain—that extends the concept of time series chains to cross-sequence scenarios for the first time. By leveraging subsequence similarity modeling, a cross-sequence alignment strategy, and a new chain-ranking criterion, the method efficiently uncovers robust anomalous evolution trends. Empirical evaluations demonstrate that the proposed approach significantly outperforms current state-of-the-art techniques across multiple datasets. Furthermore, it has been successfully deployed in an Intel manufacturing setting, where it effectively identifies complex anomalous patterns, showcasing its practical utility in real-world industrial applications.

Addressing the challenge of analyzing multivariate, irregularly sampled time series with missing values, this paper introduces PyPOTS, an open-source Python toolbox. It is the first unified framework to systematically integrate probabilistic models (e.g., VAEs, GMMs) with deep learning architectures (e.g., GRUs, Transformers), supporting four core tasks: missing value imputation, classification, clustering, and forecasting. Designed for both academic reproducibility and industrial robustness, PyPOTS features a modular architecture, >90% test coverage, CI/CD pipelines, parallelized computation, and comprehensive documentation—including interactive tutorials. Released on PyPI, Anaconda, and GitHub, it has been widely adopted in both research and industry. PyPOTS significantly lowers engineering barriers and reduces methodological replication costs for incomplete time series analysis.

This work addresses the lack of synthetic data stream generators capable of simulating real-world temporal dynamics with controllable distribution shifts and evolving causal relationships. The authors propose a time-varying synthetic data generation framework grounded in structural causal models (SCMs), which explicitly models the evolution of causal mechanisms between features and targets by dynamically adjusting SCM mapping functions and incorporating causal interventions. This approach generates non-stationary data streams that jointly exhibit covariate shift and concept drift. Notably, it is the first framework to integrate time-varying causal mechanisms with controllable drift, enabling simultaneous simulation of abrupt perturbations and gradual evolutions. Experiments demonstrate that the generated data streams exhibit realistic drift characteristics and effectively reveal performance degradation and recovery patterns of machine learning models under distributional shifts, thereby providing a reliable benchmark for evaluating model robustness.

This study addresses a key limitation of traditional time series scenario generation methods, which often produce interest rate curve paths lacking economic plausibility despite matching historical return distributions. To overcome this, the authors propose a novel framework that integrates parametric term structure models with a semi-parametric bootstrap approach. The method preserves the dynamic structure of the underlying model while resampling residuals and incorporates autoregressive or mean-reverting specifications to enhance temporal coherence of generated paths. Empirical results demonstrate that, in fixed-income applications, the proposed approach significantly outperforms conventional nonparametric techniques by simultaneously reproducing the statistical properties of yield curves accurately and generating scenarios that align with economic reasoning.

This work addresses the lack of reliable uncertainty quantification in online trend estimation for nonstationary time series by proposing a general online bootstrap method applicable to trend estimators expressed as time-window-weighted sample means—such as exponential smoothing and moving averages. Built upon asymptotic theory, the method provides the first uniform-in-time coverage guarantees for trend inference under nonstationarity, enabling adaptive anomaly detection and A/B testing in streaming data settings. Empirical evaluations demonstrate that the framework achieves well-calibrated uncertainty estimates and scales effectively across diverse nonstationary scenarios, offering a practical and real-time solution for accurate uncertainty quantification in large-scale online time series analysis.

This study addresses the limitations of existing spatial dependence diagnostics—such as Moran’s I and APLE—in effectively assessing residual spatial autocorrelation after adjusting for large-scale trends and covariates. The authors propose RESAPLE, a novel first-order approximation estimator based on restricted maximum likelihood (REML) residuals, to accurately and efficiently estimate the spatial autocorrelation parameter ρ in spatial error models. By innovatively integrating the Rayleigh quotient formulation with REML residuals, RESAPLE combines the interpretability of exploratory spatial indicators with the rigor of statistical estimation, while also offering a diagnostic tool for selecting spatial weight matrices. Under correctly specified trend models and with moderate to small sample sizes, RESAPLE demonstrates superior estimation accuracy and testing power compared to both Moran’s I and APLE, and is applicable to both regular and irregular lattice data.

Existing multistep time series foundation models output only independent marginal distributions per timestep, failing to capture genuine temporal dependency structures required for realistic joint sample paths. To address this, we propose the first copula-based single-forward-sampling framework that integrates pretrained models’ marginal forecasts with flexible copula modeling, enabling efficient generation of highly correlated, high-fidelity full-length sample paths via inverse transform sampling. Our approach circumvents the high computational cost and error accumulation inherent in autoregressive sampling, accelerating inference by several orders of magnitude. Empirically, it significantly improves path quality and prediction robustness across multiple benchmark tasks. Notably, it achieves zero-shot, one-shot generation of high-quality joint distribution samples from off-the-shelf time series foundation models—without any fine-tuning—marking the first such capability in the literature.