A Serial Independence Test by Kullback-Leibler via Quantile Symbolization

Abstract

In this article, a new consistent, and powerful test is constructed for serial independence by using quantile symbolization. The test statistic is formulated based on the Kullback-Leibler divergence, and its asymptotic distribution under the null hypothesis is proven. Moreover, the consistency of the proposed test is discussed. A simulation study compares the proposed tests efficiency (size-corrected power) with alternative tests (such as the BDS test). Ultimately, an application to the real-world data example is presented.