We propose an effcient 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 effcient 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 conrms the merits of our approach.
JEL-Codes: C12; C13; C14
Keywords: Entropy; naive bootstrap; nonlinear time series; numerical Integration; sample averaging; serial dependence; smoothed bootstrap