Testing for parameter change epochs in GARCH time series

51 Pages Posted: 22 Mar 2021

See all articles by Weining Wang

Weining Wang

affiliation not provided to SSRN; University of York

Wei Biao Wu

University of Chicago

Stefan Richter

affiliation not provided to SSRN

Date Written: February 23, 2021

Abstract

We develop a uniform test for detecting and dating the integrated or mildly explosive behaviour of a strictly stationary generalized autoregressive conditional heteroskedasticity (GARCH) process. Namely, we test the null hypothesis of a globally stable GARCH process with constant parameters against {the alternative that} there is an ``abnormal" period with changed parameter values. During this period, the parameter-value change may lead to an integrated or mildly explosive behaviour of the volatility process. It is assumed that both the magnitude and the timing of the breaks are unknown. We develop a double-supreme test for the existence of breaks, and then provide an algorithm to identify the periods of changes.
Our theoretical results hold under mild moment assumptions on the innovations of the GARCH process. Technically, the existing properties for the quasi-maximum likelihood estimation (QMLE) in the GARCH model need to be reinvestigated to hold uniformly over all possible periods of change. The key results involve a uniform weak Bahadur representation for the estimated parameters, which leads to weak convergence of the test statistic to the supreme of a Gaussian process.
In simulations we show that the test has good size and power for reasonably long time series. We apply the test to the conventional early-warning indicators of both the financial market and a representative of the emerging Fintech market, i.e. the Bitcoin returns.

Keywords: GARCH, IGARCH, Change-point Analysis, Concentration Inequalities, Uniform Test

JEL Classification: C01,C10,C22

Suggested Citation

Wang, Weining and Wang, Weining and Wu, Wei Biao and Richter, Stefan, Testing for parameter change epochs in GARCH time series (February 23, 2021). Available at SSRN: https://ssrn.com/abstract=3791556 or http://dx.doi.org/10.2139/ssrn.3791556

Weining Wang (Contact Author)

affiliation not provided to SSRN

University of York ( email )

Department of Economics and Related Studies Univer
York, YO10 5DD
United Kingdom

Wei Biao Wu

University of Chicago ( email )

1101 East 58th Street
Chicago, IL 60637
United States

Stefan Richter

affiliation not provided to SSRN

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