Optimal break tests for large linear time series models

2025-10-14

AI Summary

This paper addresses structural break detection at unknown change points in infinite-order time series models—such as AR(∞), high-dimensional linear regression, and nonparametric regression. To overcome the dual challenges of identification failure under the null and strong serial dependence in high dimensions, we develop a high-dimensional asymptotic framework, extend the Andrews–Ploberger exponential-type test, and characterize the joint asymptotic behavior of growing dimensionality and temporal dependence via a functional central limit theorem. A robust test statistic is constructed by introducing auxiliary i.i.d. Gaussian errors, and higher-order serial correlation and finite-sample bias are corrected through Monte Carlo simulation and empirical calibration. Simulation and empirical results demonstrate that the proposed method achieves substantially higher power and greater stability than existing approaches, while retaining theoretical optimality in average power and practical applicability.

Technology Category

• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Time-Series/Data Streams

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

We develop a class of optimal tests for a structural break occurring at an unknown date in infinite and growing-order time series regression models, such as AR($infty$), linear regression with increasingly many covariates, and nonparametric regression. Under an auxiliary i.i.d. Gaussian error assumption, we derive an average power optimal test, establishing a growing-dimensional analog of the exponential tests of Andrews and Ploberger (1994) to handle identification failure under the null hypothesis of no break. Relaxing the i.i.d. Gaussian assumption to a more general dependence structure, we establish a functional central limit theorem for the underlying stochastic processes, which features an extra high-order serial dependence term due to the growing dimension. We robustify our test both against this term and finite sample bias and illustrate its excellent performance and practical relevance in a Monte Carlo study and a real data empirical example.

Problem

• Optimal tests for structural breaks in large time series
• Handling identification failure under no-break null hypothesis
• Robust testing against high-dimensional serial dependence and bias

Innovation

• Optimal tests for structural breaks in large models
• Handles growing-dimensional time series with dependence
• Robust against high-order serial dependence and bias