Chernoff, Bhattacharyya, Rényi and Sharma-Mittal Divergence Analysis for Gaussian Stationary ARMA Processes

The purpose of this paper is first to derive the expressions of the Chernoff, Bhattacharyya, Renyi and Sharma-Mittal divergences when comparing two probability density functions of vectors storing k consecutive samples of Gaussian ARMA processes. This can be useful for process comparison or statistical change detection issue. Then, we analyze the behaviors of the divergences when k increases and tends to infinity by using some results related to ARMA processes such as the Yule-Walker equations. Comments and illustrations are given.