Conditional variance model checking

This paper discusses the problem of fitting a parametric model to the conditional variance function in a class of heteroscedastic regression models. The proposed test is based on the supremum of the Khmaladze type martingale transformation of a certain partial sum process of calibrated squared residuals. Asymptotic null distribution of this transformed process is shown to be the same as that of a time transformed standard Brownian motion. Test is shown to be consistent against a large class of fixed alternatives and to have nontrivial asymptotic power against a class of nonparametric n - 1 / 2 -local alternatives, where n is the sample size. Simulation studies are conducted to assess the finite sample performance of the proposed test and to make a finite sample comparison with an existing test.