Checking nonlinear heteroscedastic time series models

A procedure for testing simultaneously, the parametric forms of the conditional mean and the conditional variance functions of a real-valued heteroscedastic time series model is proposed. The Wald test statistic is based on a vector whose components are suitable normalized sums of some weighted residual series. The test is consistent under some fixed alternatives. The local power under two sequences of local alternatives is studied. A LAN property for the parametric model of interest is also established. Experiment conducted shows that the test performs well on the examples tested.