On the inversion of an autoregressive process of finite order

Abstract

In this paper we are interested by the inversion of any stationary and causal autoregressive process of order p, we give some recurrence relations satisfied by the coefficients of the infinite moving average process representation in the sense of Wold decomposition. We compute explicit formula of these coefficients and the corresponding auto-covariance function and we give the minimal value of q in mean square approximation of this autoregressive process with a moving average process of order q-1. The obtained results are explained by examples from the literature and our choice.