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Residual-Based Rank Specification Tests for AR-GARCH Type Models

52 Pages Posted: 20 Jul 2013  

Elena Andreou

University of Cyprus - Department of Economics

Bas J. M. Werker

Tilburg University - Center for Economic Research (CentER)

Multiple version iconThere are 2 versions of this paper

Date Written: July 19, 2013

Abstract

This paper derives the asymptotic distribution for a number of rank-based and classical residual specification tests in AR-GARCH type models. We consider tests for the null hypotheses of no linear and quadratic serial residual autocorrelation, residual symmetry, and no structural breaks. For these tests we show that, generally, no size correction is needed in the asymptotic test distribution when applied to AR-GARCH type residuals obtained through QMLE estimation. To be precise, we give exact expressions for the limiting null distribution of the test statistics applied to residuals, and find that standard critical values often lead to conservative tests. For this result, we give simple sufficient conditions. Simulations show that our asymptotic approximations work well for a large number of AR-GARCH models and parameter values. We also show that the rank-based tests often, though not always, have superior power properties over the classical tests, even if they are conservative. We thereby provide a useful extension to the econometrician’s toolkit. An empirical application illustrates the relevance of these tests to the AR-GARCH models for the weekly stock market return indices of some major and emerging countries.

Keywords: Conditional heteroskedasticity, Linear and quadratic residual auto- correlation tests, Model misspecification test, Nonlinear time series, Parameter constancy, Residual symmetry tests

JEL Classification: C22, C32, C51, C52

Suggested Citation

Andreou, Elena and Werker, Bas J. M., Residual-Based Rank Specification Tests for AR-GARCH Type Models (July 19, 2013). Available at SSRN: https://ssrn.com/abstract=2295906 or http://dx.doi.org/10.2139/ssrn.2295906

Elena Andreou

University of Cyprus - Department of Economics ( email )

75 Kallipoleos Street
P.O. Box 20537
1678 Nicosia
Cyprus
+357 2 892449 (Phone)
+357 2 892432 (Fax)

Bas J.M. Werker (Contact Author)

Tilburg University - Center for Economic Research (CentER) ( email )

Econometrics and Finance Group
5000 LE Tilburg
Netherlands

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