A martingale-difference-divergence-based test for specification

- We propose a novel martingale-difference-divergence-based test for specification.
- The test does not require any nonparametric estimation.
- The test is applicable even if we have many covariates in the regression model.
- The test has superb finite sample performance and dominates its competitors.

In this paper we propose a novel consistent model specification test based on the martingale difference divergence (MDD) of the error term given the covariates. The MDD equals zero if and only if error term is conditionally mean independent of the covariates. Our MDD test does not require any nonparametric estimation under the alternative and it is applicable even if we have many covariates in the regression model. We establish the asymptotic distributions of our test statistic under the null and a sequence of Pitman local alternatives converging to the null at the usual parametric rate. Simulations suggest that our MDD test has superb performance in terms of both size and power and it generally dominates several competitors. In particular, it is the only test that has well controlled size in the presence of many covariates and reasonable power against high frequency alternatives as well.