Estimation for autoregressive processes with positive innovations

Abstract

We consider stationary autoregressive processes of order p which have positive parameters and positive innovations. The main results concern the rate of consistency of parameter estimators for the case p = 2. These estimators are defined in terms of estimating equations. Relevant asymptotic theory is developed in the wider context of vector autoregressive processes with positive innovations having a distribution with regularly varying left or right tails. These weak convergence results may be of independent interest.