首页|Testing for parameter change epochs in GARCH time series
Testing for parameter change epochs in GARCH time series
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NETL
NSTL
Oxford Univ Press
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 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. Simulations in the Appendix 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.
GARCHIGARCHchange-point analysisconcentration inequalitiesuniform test
STEFAN RICHTER、WEINING WANG、WEI BIAO WU
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Heidelberg University, Institute of Applied Mathematics, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
University of York, York YO10 5DD, UK
Department of Statistics and the College, University of Chicago, USA
NETL
NSTL
Oxford Univ Press
