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

Bas J M Werker and Elena Andreou

No 9583, CEPR Discussion Papers from C.E.P.R. Discussion Papers

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: Parameter constancy; Conditional heteroskedasticity; Linear and quadratic residual autocorrelation tests; Model misspecification test; Nonlinear time series; Residual symmetry tests (search for similar items in EconPapers)
JEL-codes: C22 C32 C51 C52 (search for similar items in EconPapers)
Date: 2013-08
New Economics Papers: this item is included in nep-ecm and nep-ets
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