Inference in Univariate and Bivariate Autoregressive Models with Non-Normal Innovations

‎In this paper we consider the estimation, ‎order and model selection of autoregressive time series model which may be driven by non-normal innovations. ‎The paper makes two contributions. ‎First, ‎we consider the method of moments for a univariate and also a bivariate time series model; the importance of using the method of moments is that it can provide us with consistent estimates easily for any model order and for any kind of distribution that we can assume for the non-normal innovations‎. ‎Second, ‎we provide methods 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. ‎Our results show that although the performance of modified maximum likelihood estimators is better than method of moments estimators when the sample size is small but both methods have approximately same performance as the sample size increase and in misspecification case. ‎Also It is shown that focussed information criterion is an appropriate criterion for model selection for autoregressive models with non-normal innovations based on the method of moments estimators.