On the exact moments of non-standard asymptotic distributions in non stationary autoregressions with dependent errors

In this paper we derive the exact moments of the asymptotic distributions of the OLS estimate and t-statistic in an unstable AR(1) with dependent errors. We can therefore establish theoretically and without simulations, the distortions induced by the presence of non iid errors on inferences as judged by their impact on the moments of the limiting distributions. In addition we study the relationship between the number of lagged dependent variables required for matching the moments of the distribution in the "approximately iid errors" model with those occuring in the purely iid case. Our framework allows us to distinguish explicitly between different types of error processes and study their implications for the lag length selection. A very accurate normal approximation also allows us to obtain approximate magnitudes for the size distortions when the iid based distributions are used for inferences.