Testing serial independence via density-based measures of divergence

This article reviews some nonparametric serial independence tests based on measures of divergence between densities. Among others, the well-known Kullback-Leibler, Hellinger, Tsallis, and Rosenblatt divergences are analyzed. Moreover, their copula-based version is taken into account. Via a wide simulation study, the performances of the considered serial independence tests are compared under different settings. Both single-lag and multiple-lag testing procedures are investigated to find out the best "omnibus" solution