Cavaliere, G. orcid.org/0000-0002-2856-0005, Perera, I. and Rahbek, A. (2024) Specification tests for GARCH processes with nuisance parameters on the boundary. Journal of Business & Economic Statistics, 42 (1). pp. 197-214. ISSN 0735-0015
Abstract
This paper develops tests for the correct specification of the conditional variance function in GARCH models when the true parameter may lie on the boundary of the parameter space. The test statistics considered are of Kolmogorov-Smirnov and Cramér-von Mises type, and are based on empirical processes marked by centered squared residuals. The limiting distributions of the test statistics depend on unknown nuisance parameters in a non-trivial way, making the tests difficult to implement. We therefore introduce a novel bootstrap procedure which is shown to be asymptotically valid under general conditions, irrespective of the presence of nuisance parameters on the boundary. The proposed bootstrap approach is based on shrinking of the parameter estimates used to generate the bootstrap sample toward the boundary of the parameter space at a proper rate. It is simple to implement and fast in applications, as the associated test statistics have simple closed form expressions. Although the bootstrap test is designed for a data generating process with fixed parameters (i.e., independent of the sample size n), we also discuss how to obtain valid inference for sequences of DGPs with parameters approaching the boundary at the n−1/2 rate. A simulation study demonstrates that the new tests: (i) have excellent finite sample behaviour in terms of empirical rejection probabilities under the null as well as under the alternative; (ii) provide a useful complement to existing procedures based on Ljung-Box type approaches. Two data examples illustrate the implementation of the proposed tests in applications.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 American Statistical Association. This is an author-produced version of a paper subsequently published in Journal of Business & Economic Statistics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Bootstrap; Kolmogorov-Smirnov; Cramér-von Mises; Marked empirical process |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Social Sciences (Sheffield) > Department of Economics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 15 Feb 2023 16:30 |
Last Modified: | 27 Sep 2024 11:32 |
Status: | Published |
Publisher: | Informa UK Limited |
Refereed: | Yes |
Identification Number: | 10.1080/07350015.2023.2173206 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:196443 |