Testing serial independence via densitybased measures of divergence

Abstract This article reviews the nonparametric serial independence tests based on measures of divergence between densities. Among others, the well-known Kull-back-Leibler, Hellinger and Tsallis divergences are analyzed. Moreover, the copula-based version of the considered divergence functionals is defined and taken into account. In order to implement serial independence tests based on these divergence functionals, it is necessary to choose a density estimation technique, a way to com-pute p-values and other settings. Via a wide simulation study, the performance of the serial independence tests arising from the adoption of the divergence function-als with different implementation is compared. Both single-lag and multiple-lag test procedures are investigated in order to find the best solutions in terms of size and power