Jeffrey's divergence between moving-average and autoregressive models

Abstract

This paper deals with model comparison based on the Jeffrey's divergence (JD). More particularly, after providing the JD between the joint distributions of k consecutive values of a white noise and the ones of a real moving-average or autoregressive model, the JD between real 1st-order MA and real 1st-order AR models is studied. Except when the 1st MA parameter is equal to 1, we show that, after a transient period, the JD between both models is incremented by a constant value that depends on the model parameters while k is incremented by 1. The JD is hence characterized by this increment and it is not necessary to consider a lot of samples.