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Title: Residual-based Rank Specification Tests for AR-GARCH type models

Author(s): Elena Andreou and Bas J M Werker

Publication Date: August 2013

Keyword(s): conditional heteroskedasticity, linear and quadratic residual autocorrelation tests, model misspecification test, nonlinear time series, parameter constancy and residual symmetry tests

Programme Area(s): Financial Economics

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.

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Bibliographic Reference

Andreou, E and Werker, B. 2013. 'Residual-based Rank Specification Tests for AR-GARCH type models'. London, Centre for Economic Policy Research. https://cepr.org/active/publications/discussion_papers/dp.php?dpno=9583