An efficient integrated nonparametric entropy estimator of serial dependence

We propose an efficient numerical integration-based nonparametric entropy estimator for serial dependence and show that the new entropy estimator has a smaller asymptotic variance than Hong and White.s (2005) sample average-based estimator. This delivers an asymptotically more efficient test for serial dependence. In particular, the uniform kernel gives the smallest asymptotic variance for the numerical integration-based entropy estimator over a class of positive kernel functions. Moreover, the naive bootstrap can be used to obtain accurate inferences for our test, whereas it is not applicable to Hong and White.s (2005) sample averaging approach. A simulation study confirms the merits of our approach.