Moment Estimation and Model Selection in Univariate Autoregressive Models with Non-Normal Innovations

In this paper we consider the estimation, order and model selection of autoregressive model which may be driven by non-normal innovations. We provide method for order and model selection, i.e. for selecting the order of the autoregression and the model for the innovation’s distribution. Our analysis provides analytic results on the asymptotic distribution of the method of moments estimators and also computational results via simulations. It is shown that focussed information criterion is appropriate for model selection arising from autoregressive models with non-normal innovations based on the method of moments estimators.