A Simple Asymptotic Analysis of Residual-Based Statistics
University of Cyprus - Department of Economics
Bas J. M. Werker
Tilburg University - Center for Economic Research (CentER)
CentER Discussion Paper No. 2003-118
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.
Number of Pages in PDF File: 29
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, C52working papers series
Date posted: July 16, 2004
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