Variable Selection Based Testing for Parameter Changes in Regression with Autoregressive Dependence

Abstract

We consider a regression model with autoregressive terms and propose significance tests for the detection of change points in this model. Our tests are applicable to both low- or moderate dimension and to high-dimension with sparse regressors. The dimension may be high from the practical point of view of economic and business applications, but in our theoretical framework it is fixed. To accommodate practically high dimension, variable selection is incorporated as an integral part of our approach. The regressors and the errors can exhibit general nonlinear dependence and the model incorporates autoregressive dependence. We develop asymptotic justification and evaluate the performance of the tests both on simulated and real economic data. We test for and estimate changes in responses to risk factors of a U.S. energy stocks portfolio and the Industrial Production index. We relate our findings to macroeconomic policy changes and global impact events.

Keywords:

• Change points
• Significance test
• Time series regression
• Variable selection

Supplementary Materials

Additional supplementary material may be found online in the supplemental material tab for this article. It contains the proofs of the results stated in Section 3 (Section A), additional power curves graphs (Section B), the definitions of the response variable and the explanatory variables used in Section 5.1 (Section C), and the data availability statement (Section D).

Acknowledgments

We thank the Digital Economy Laboratory at the University of International Business and Economics for providing a high-performance computer, which enabled the execution of our numerical work.

Disclosure Statement

The authors do not declare any conflict of interest.

Notes

1 For more details, please see the website https://www.archives.gov/federal-register/codification/executive-order/12287.html (June 8, 2022).

Additional information

Funding

This research was partially supported by the United States National Science Foundation grants DMS–1923142, DMS–1914882 and DMS–2123761. Shanglin Lu was supported by the National Natural Science Foundation of China (No. 72303032) and the Fundamental Research Funds for the Central Universities in UIBE (22QD07).