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 Bierens ( , 1984 , under a class of %n-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, for a class of "large" local alternatives the consistent ICM test is more powerful than the parametric t-test in a neighborhood of the parametric alternative involved. Furthermore, 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.
REF also characterizes the asymptotic null distribution of a general class of realvalued weighting functions.
Asymptotic Theory of Integrated Conditional Moment Tests
Econometrica
Mathematics