Asymptotic Distribution-Free Diagnostic Tests for Heteroskedastic Time Series Models
Center for Applied Economics and Policy Research Paper No. 019-2009
33 Pages Posted: 21 Oct 2009
Date Written: September 10, 2009
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 in nite-dimensional, and consistent against a class of Pitman's local alternatives converging at the parametric rate n1=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.
Keywords: Time series models, model speci cation, ARMA-GARCH mod- els, S&P 500
JEL Classification: C12, C52
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