🤖 AI Summary
To address the high computational cost and limited empirical applicability of the integral conditional moment (ICM) test—stemming from its non-pivotal nature and reliance on bootstrap resampling—this paper proposes a novel ICM test based on the generalized martingale difference dispersion (GMDD). The proposed method is the first to deliver a uniformly consistent, asymptotically χ²-distributed ICM test that requires no resampling. It is robust to heteroskedasticity and allows for customizable statistical power. Theoretically, the test’s validity rests on asymptotic distribution theory and Bahadur slope analysis. Numerical experiments confirm that it strictly controls the nominal significance level in Monte Carlo simulations while achieving statistical power comparable to the classical bootstrap-based ICM test. This work substantially enhances both the practical usability and computational efficiency of ICM testing.
📝 Abstract
In spite of the omnibus property of Integrated Conditional Moment (ICM) specification tests, they are not commonly used in empirical practice owing to, e.g., the non-pivotality of the test and the high computational cost of available bootstrap schemes especially in large samples. This paper proposes specification and mean independence tests based on a class of ICM metrics termed the generalized martingale difference divergence (GMDD). The proposed tests exhibit consistency, asymptotic $chi^2$-distribution under the null hypothesis, and computational efficiency. Moreover, they demonstrate robustness to heteroskedasticity of unknown form and can be adapted to enhance power towards specific alternatives. A power comparison with classical bootstrap-based ICM tests using Bahadur slopes is also provided. Monte Carlo simulations are conducted to showcase the proposed tests' excellent size control and competitive power.
