A Simple Asymptotic Analysis of Residual-Based Statistics

CentER Discussion Paper No. 2003-118

29 Pages Posted: 16 Jul 2004

See all articles by Elena Andreou

Elena Andreou

University of Cyprus - Department of Economics

Bas J. M. Werker

Tilburg University - Center for Economic Research (CentER)

Date Written: 2003

Abstract

What's the asymptotic null distribution of a rank-based serial autocorrelation test applied to residuals of an estimated GARCH model? What's the limiting distribution of estimated ACD parameters applied to the residuals of some first-stage modelling procedure? This paper addresses the often occuring situation in econometrics of applying standard statistics to residuals instead of innovations. The paper provides a simple and unified way of calculating the necessary adjustment in the limiting distribution, be it of tests or estimators. On the technical side, we also provide a novel approach to this problem using Le Cam's theory of convergence of experiments (in this paper restricted to Gaussian shift experiments). The resulting formula is simple and the regularity conditions required fairly minimal. Numerous examples show the strength and wide applicability of our approach.

Keywords: Asymptotic size, discretized estimators, goodness-of-fit tests, local asymptotic normality, rank statistics, structural break tests, temporal dependence tests, two-stage inference

JEL Classification: C32, C51, C52

Suggested Citation

Andreou, Elena and Werker, Bas J.M., A Simple Asymptotic Analysis of Residual-Based Statistics (2003). CentER Discussion Paper No. 2003-118, Available at SSRN: https://ssrn.com/abstract=556953 or http://dx.doi.org/10.2139/ssrn.556953

Elena Andreou (Contact Author)

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

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

Econometrics and Finance Group
5000 LE Tilburg
Netherlands

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