An efficient integrated nonparametric entropy estimator of serial dependence

【Abstract】We propose an efcient numerical integration-based nonparametric entropy estimatorfor serialdependence and showthat the new entropy estimatorhas a smaller asymptotic variance than Hong and White's (2005) sample averagebased estimator. This delivers an asymptotically more efcient 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.Wang acknowledges fnancial supports from the National Science Foundation of China (No. 71401160, 71371160), the Ministry of Education of Humanities and Social Sciences Project of China (No. 14YJC790120), Fujian Provincial Key Laboratory of Statistics (Xiamen University, No. 2016003)