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

Wenzhi Yang, Yueting Xu, Xiaoping Shi, Qiong Li

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.

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

Abstract

This paper investigates change-point of variance in panel data models with time series of -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.
Paper Structure (11 sections, 49 equations, 3 figures, 2 tables)

This paper contains 11 sections, 49 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Panel Variance Change-Point Models and Test Construction
  3. Variance Change-Point Test of Li et al. (2015)
  4. Motivation for a Modified Test
  5. Modeling framework
  6. Comparison of test construction
  7. Power comparison
  8. Model Assumptions and Theoretical Results
  9. Simulations
  10. The Real Data Analysis
  11. Conclusion and Discussion

Figures (3)

  • Figure 1: Comparison of the panel variance change statistics $T_V$ and $T_U$ under a sparse variance change model. The left panel displays the empirical distributions of $T_V$ and $T_U$ based on 1000 Monte Carlo replications. The right panel shows the distribution of the difference $T_U - T_V$.
  • Figure 2: The adjusted closing price chart and variance change-point of Shanghai Shenzhen CSI 300 index components, 296 stocks from 2006-01-01 to 2016-12-31
  • Figure 3: The histogram of variance change-points with 'cpt.var' method for 296 stocks from 2006-01-01 to 2016-12-31