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ASYMPTOTIC DISTRIBUTION-FREE DIAGNOSTIC TESTS FOR HETEROSKEDASTIC TIME SERIES MODELS

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 of possibly nonlinear heteroskedastic time series models, including but not restricted to ARMA-GARCH models. We propose omnibus tests based on functionals of certain weighted standardized residual empirical processes. The new tests are asymptotically distribution-free, suitable when the conditioning set is infinite-dimensional, and consistent against a class of Pitman’s local alternatives converging at the parametric rate n−1/2, with n the sample size. A Monte Carlo study shows that the simulated level of the proposed tests is close to the asymptotic level already for moderate sample sizes and that tests have a satisfactory power performance. Finally, we illustrate our methodology with an application to the well-known S&P 500 daily stock index. The paper also contains an asymptotic uniform expansion for weighted residual empirical processes when initial conditions are considered, a result of independent interest.

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 Nacional de I+D+I, reference number SEJ2007-62908, and by the Spanish Ministerio de Educación y Ciencia, reference number SEJ2005-07657/ECON. I would like to thank Miguel A. Delgado, Oliver Linton, Carlos Velasco, and two anonymous referees for helpful comments. I also thank Wenceslao González-Manteiga for pointing out an important reference. All errors are mine.

References

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