TESTING GOODNESS OF FIT BASED ON DENSITIES OF GARCH INNOVATIONS

Lajos Horvath and Ričardas Zitikis

Econometric Theory, 2006, vol. 22, issue 3, 457-482

Abstract: Testing goodness (or lack) of fit for distributions of observable and nonobservable random variables is one of the main topics in statistics. When they exist, the corresponding density functions and their shapes allow researchers to easily recognize the underlying distribution functions. The present paper is concerned with the densities of (unobservable) generalized autoregressive conditional heteroskedasticity (GARCH) innovations and also with developing goodness-of-fit tests for the densities. Specifically, we construct and investigate large-sample properties of a kernel-type density estimator for GARCH innovations based on (observable) residuals.The authors sincerely thank the Co-Editor Oliver Linton and three anonymous referees for constructive criticism and suggestions that helped us to prepare a much revised version of the original manuscript. The feedback by participants of the Conference on Statistical Models for Financial Data at the University of Graz in May 2004 is also greatly appreciated. The research of the first author was partially supported by NSF grant INT-0223262 and NATO grant PST.EAP.CLG 980599. The research of the second author was partially supported by a Discovery Research Grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada.

Date: 2006
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