ASYMPTOTIC THEORY OF INTEGRATED CONDITIONAL MOMENT TESTS

In this paper we derive the asymptotic distribution of the test statis tic of a generalized version of the integrated conditional moment (ICM ) test of Bierens (1982, 1984), under a class of root n-local alternat ives, where n is the sample size. The generalized version involved inc ludes neural network tests as a special case, and allows for testing m isspecification of dynamic models. It appears that the ICM test has no ntrivial local power. Moreover, for a class of ''large'' local alterna tives the consistent ICM test is more powerful than the parametric t t est in a neighborhood of the parametric alternative involved. Furtherm ore, under the assumption of normal errors the ICM test is asymptotica lly admissible, in the sense that there does not exist a test that is uniformly more powerful. The asymptotic size of the test is case-depen dent: the critical values of the test depend on the data-generating pr ocess. In this paper we derive case-independent upperbounds of the cri tical values.