On Computing Jeffrey’s Divergence Between Time-Varying Autoregressive Models

Abstract

Autoregressive (AR) and time-varying AR (TVAR) models are widely used in various applications, from speech processing to biomedical signal analysis. Various dissimilarity measures such as the Itakura divergence have been proposed to compare two AR models. However, they do not take into account the variances of the driving processes and only apply to stationary processes. More generally, the comparison between Gaussian processes is based on the Kullback-Leibler (KL) divergence but only asymptotic expressions are classically used. In this letter, we suggest analyzing the similarities of two TVAR models, sample after sample, by recursively computing the Jeffrey's divergence between the joint distributions of the successive values of each TVAR model. Then, we show that, under some assumptions, this divergence tends to the Itakura divergence in the stationary case.