Jeffrey's divergence between moving-average models that are real or complex, noise-free or disturbed by additive white noises

Abstract

Time series models play a key-role in many applications from biomedical signal analysis to applied econometric. The purpose of this paper is to compare 1st-order moving-average (MA) models by using dissimilarity measures such as the Jeffrey's divergence (JD), which is the symmetric version of the Kullback–Leibler divergence (KL). The MA models can be real or complex. They can also be disturbed by additive white noises or not. Analytical expressions are first proposed and analyzed. Then, the JD is used to compare more than two 1st-order MA models in order to extract MA model subsets. In the latter case, we suggest analyzing the higher-order singular values of a tensor defined from the JDs between models over time to deduce the number of subsets and their cardinals. Simulation results illustrate the theoretical analysis.