Adaptive Change Point Inference for High Dimensional Time Series with Temporal Dependence

2025-11-03

AI Summary

This paper addresses change-point inference in high-dimensional time series, where the sparsity of change points is unknown and temporal dependence is present. To tackle these challenges, we propose a max-L₂-norm-based test statistic and—novelly for this domain—introduce the Cauchy combination method, adaptively fusing it with the max-L∞ test to achieve unified, robust detection under both dense and sparse alternative hypotheses. We establish asymptotic independence between the new statistic and existing max-L∞ statistics, thereby overcoming the strong reliance of conventional methods on prespecified sparse structures. Theoretical analysis confirms validity under general dependence structures, while simulations and empirical studies demonstrate substantial improvements in detection sensitivity and stability in high-dimensional settings—particularly under weak signals and strong temporal dependence.

Technology Category

• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

This paper investigates change point inference in high-dimensional time series. We begin by introducing a max-$L_2$-norm based test procedure, which demonstrates strong performance under dense alternatives. We then establish the asymptotic independence between our proposed statistic and the two max-$L_infty$-based statistics introduced by Wang and Feng (2023). Building on this result, we develop an adaptive inference approach by applying the Cauchy combination method to integrate these tests. This combined procedure exhibits robust performance across varying levels of sparsity. Extensive simulation studies and real data analysis further confirm the superior effectiveness of our proposed methods in the high-dimensional setting.

Problem

• Develops adaptive change point inference for high-dimensional time series
• Establishes asymptotic independence between max-norm test statistics
• Integrates multiple tests for robust performance across sparsity levels

Innovation

• Max-L2-norm test for dense change points
• Asymptotic independence with max-L-infinity statistics
• Cauchy combination method for adaptive inference