Specification tests for GARCH processes

Giuseppe Cavaliere, Indeewara Perera and Anders Rahbek
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Indeewara Perera: Department of Economics, The University of Sheffield

No 21-06, Discussion Papers from University of Copenhagen. Department of Economics

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 a certain empirical process marked by centered squared residuals. The limiting distributions of the test statistics are not free from (unknown) nuisance parameters, and hence critical values cannot be tabulated. A novel bootstrap procedure is proposed to implement the tests; it 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. 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 are considered to illustrate the tests.

Keywords: GARCH model; bootstrap; specification test; Kolmogorov-Smirnov test; Cramér-von Mises test; marked empirical process; nuisance parameters on the boundary (search for similar items in EconPapers)
Date: 2021
New Economics Papers: this item is included in nep-ecm and nep-ets
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Working Paper: Specification tests for GARCH processes (2021)
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