The Asymptotic Mean Squared Error of the AR Model with a General form of Time Trend Involved

Abstract

We prove a characterization theorem for minimal eigunvalues of sample covariance matrices. This result enables us to derive nagative moment bounds for Fisher infromation matrices in autoregressive (AR) models around deterministic time trends, which in turn play a crucial role in calculating the mean squared prediction error (MSPE) of the aforementioned models.