Asymptotic distribution-free diagnostic tests for heteroskedastic time series models

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 Pitmans 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. (copyright) 2009 Cambridge University Press.

Asymptotic distribution-free diagnostic tests for heteroskedastic time series models Articles