  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.
