Asymptotic theory of integrated conditional moment tests

In this paper we derive the asymptotic distribution of the test statistic of a generalized version of the integrated conditional moment (ICM) test of Bierens (1982, 1984), under a class of Vn-local alternatives, where n is the sample size. The generalized version involved includes neural network tests as a special case, and allows for testing misspecification of dynamic models. It appears that the ICM test has nontrivial local power. Moreover, we show that under the assumption of normal errors the ICM test is asymptotically admissible, in the sense that there does not exist a test that is uniformly more powerful. The asymptotic size of the test is case-dependent: the critical values of the test depend on the data-generating process. In this paper we derive case-independent upperbounds of the critical values