Bootstrap specification tests for dynamic conditional distribution models

This paper proposes bootstrap based tests for the specification of a given parametric conditional distribution in autoregressive time series with GARCH-type disturbances. The tests are based on an estimated residual empirical process and are implemented by parametric bootstrap. We show that the proposed tests are asymptotically valid, consistent, and have nontrivial asymptotic power against a large proportion of local alternatives. Our approach relies on non-primitive regularity conditions and certain properties of exponential almost sure convergence. The regularity conditions are shown to be satisfied by GARCH(p,q); this technique of verification is applicable to other models as well. In our Monte Carlo study, the proposed tests performed well and better than several competing tests, including the information matrix test. A real data example illustrates the testing procedure.