A Consistent ICM-based $χ^2$ Specification Test

In spite of the omnibus property of Integrated Conditional Moment (ICM) specification tests, their use is not common in empirical practice owing to (1) the non-pivotal nature of the test and (2) the high computational cost of available bootstrap schemes in large samples. Moreover, the local power of ICM tests is only substantial within a finite-dimensional space usually unbeknownst to the researcher. Based on a class of newly developed ICM metrics called the generalized martingale difference divergence (GMDD), this paper proposes a conditional moment and specification test that is consistent, asymptotically $\chi^2$ distributed under the null, and computationally efficient. The test also accounts for heteroskedasticity of unknown form and can be enhanced to augment power in the direction of given alternatives. Besides showing significant computational gains of the proposed test, Monte Carlo simulations demonstrate their good size control and power performance comparable to bootstrap-based ICM tests.