Asymptotic Distribution-Free Diagnostic Tests for Heteroskedastic Time Series Models

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 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 Classifications: C12, C52

Working Paper Series