Testing Serial Independence via Density-Based Measures of Divergence

This article reviews the nonparametric serial independence tests based on measures of divergence between densities. Among others, the well-known Kullback-Leibler, Hellinger and Tsallis divergences are analyzed.Moreover, the copulabased 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 compute p-values and other settings. Via a wide simulation study, the performance of the serial independence tests arising from the adoption of the divergence functionals 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.