Detecting changes in GARCH(1,1) processes without assuming stationarity

Horváth, L. and Wang, S. ORCID: https://orcid.org/0000-0003-2113-5521 (2025) Detecting changes in GARCH(1,1) processes without assuming stationarity. Econometric Theory. ISSN 0266-4666 doi: 10.1017/S026646662510011X

Abstract/Summary

This paper develops a new test to detect changes in GARCH(1,1) processes without imposing a stationary assumption. Specifically, the procedure tests the null hypothesis of a GARCH process with constant parameters, either in (strictly) stationary or explosive regimes, against the alternative hypothesis of parameter changes. We derive the limiting distribution of the test statistics and establish their asymptotic consistency. Monte Carlo simulations show that the proposed test has good size control and high power. We demonstrate a prototype application on a small group of stocks and report a further extensive application to more than ten thousand U.S. stocks.