Richter, Stefan, Wang, Weining and Wu, Wei Biao (2023) Testing for parameter change epochs in GARCH time series. Econometrics Journal. pp. 467-491. ISSN 1368-4221
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2023 |
Dates: |
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Institution: | The University of York |
Academic Units: | The University of York > Faculty of Social Sciences (York) > Economics and Related Studies (York) |
Depositing User: | Pure (York) |
Date Deposited: | 08 Mar 2021 10:50 |
Last Modified: | 26 Nov 2024 00:49 |
Published Version: | https://doi.org/10.1093/ectj/utad006 |
Status: | Published |
Refereed: | Yes |
Identification Number: | 10.1093/ectj/utad006 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:171905 |
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Description: Testing for parameter change epochs in GARCH time series
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