Consistent and powerful CUSUM change-point test for panel data with changes in variance

2026-03-12

AI Summary

This study addresses the limited power of existing methods in detecting variance breaks—particularly under sparse change scenarios—in panel data. To overcome this challenge, the authors propose a unified test based on CUSUM statistics and individual differencing, tailored for α-mixing time series panel data. By deriving the asymptotic distributions under both the null and alternative hypotheses, the method maintains high testing power even when variance change points are sparse. Theoretical analysis and extensive simulations demonstrate its superior performance over current approaches under both Gaussian and Gamma error structures. Empirical application to CSI 300 constituent stock data successfully identifies meaningful variance change points and uncovers their underlying economic drivers.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

This paper investigates change-point of variance in panel data models with time series of $α$-mixing. Based on the cumulative sum (CUSUM) method and the individual differences, we construct a CUSUM test for panel data models to detect variance changes. Under the null hypothesis, we derive the limit distribution of this test, which can be used to detect the change-point of variance. Under the alternative hypothesis, the limit behavior of the CUSUM test is also derived. To validate the performance of the test, we conducted simulation analyses on with Gaussian and Gamma errors. The results demonstrate that this testing method significantly outperforms existing approaches, particularly in detecting sparse variance changes. Finally, we conducted a practical case study using panel data from the Shanghai Shenzhen CSI 300 Index Components. Not only did we successfully identify the change-points of variance, but we also delved deeper into the underlying economic drivers behind these changes.

Problem

• change-point
• variance
• panel data
• CUSUM
• α-mixing

Innovation

• CUSUM test
• panel data
• variance change-point
• α-mixing
• sparse change detection