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ASYMPTOTIC DISTRIBUTION-FREE DIAGNOSTICTESTS FOR HETEROSKEDASTIC TIME SERIESMODELS

Published online by Cambridge University Press:  26 October 2009

J. Carlos Escanciano
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Abstract

This article investigates model checks for a class ofpossibly nonlinear heteroskedastic time seriesmodels, including but not restricted to ARMA-GARCHmodels. We propose omnibus tests based onfunctionals of certain weighted standardizedresidual empirical processes. The new tests areasymptotically distribution-free, suitable when theconditioning set is infinite-dimensional, andconsistent against a class of Pitman’s localalternatives converging at the parametric raten−1/2, withn the sample size. A Monte Carlostudy shows that the simulated level of the proposedtests is close to the asymptotic level already formoderate sample sizes and that tests have asatisfactory power performance. Finally, weillustrate our methodology with an application tothe well-known S&P 500 daily stock index. Thepaper also contains an asymptotic uniform expansionfor weighted residual empirical processes wheninitial conditions are considered, a result ofindependent interest.

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Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 3 , June 2010 , pp. 744 - 773
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

Research was funded by the Spanish Plan Nacionalde I+D+I, reference number SEJ2007-62908, and bythe Spanish Ministerio de Educación y Ciencia,reference number SEJ2005-07657/ECON. I would liketo thank Miguel A. Delgado, Oliver Linton, CarlosVelasco, and two anonymous referees for helpfulcomments. I also thank Wenceslao González-Manteigafor pointing out an important reference. Allerrors are mine.

References

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