Studying Three Families of Divergences to Compare Wide-Sense Stationary Gaussian Arma Processes

In this paper, we aim at analyzing the differences between three families of divergences used to compare probability density functions of Gaussian random vectors storing k consecutive samples of wide-sense stationary ARMA processes. There may be various applications: signal classification, statistical change detection, etc. Among the families that are studied, we propose to look at the α-divergence, the β-divergence and the γ-divergence. We first provide the expression of the divergences in the Gaussian case and then express their divergence increments, i.e. the differences between the divergences computed for k + 1 and k consecutive samples. Finally, we analyze how these divergence increments evolve when k increases and tends to infinity.