Online Bootstrap Inference for the Trend of Nonstationary Time Series

2026-02-27

AI Summary

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.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Programming
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

This article proposes an online bootstrap scheme for nonparametric level estimation in nonstationary time series. Our approach applies to a broad class of level estimators expressible as weighted sample averages over time windows, including exponential smoothing methods and moving averages. The bootstrap procedure is motivated by asymptotic arguments and provides well-calibrated uniform-in-time coverage, enabling scalable uncertainty quantification in streaming or large-scale time-series settings. This makes the method suitable for tasks such as adaptive anomaly detection, online monitoring, or streaming A/B testing. Simulation studies demonstrate good finite-sample performance of our method across a range of nonstationary scenarios. In summary, this offers a practical resampling framework that complements online trend estimation with reliable statistical inference.

Problem

• online bootstrap
• nonstationary time series
• trend estimation
• uncertainty quantification
• statistical inference

Innovation

• online bootstrap
• nonstationary time series
• nonparametric estimation
• uncertainty quantification
• streaming inference