Asymptotically optimal AR spectral estimate for multistep prediction

Abstract

This paper discusses the concept of asymptotic optimality from the frequency domain point of view making use of the direct method for multiple prediction. In particular, it is shown that with the use of a new autoregressive model selection at each prediction time h, the asymptotic lower bound of the integrated relative squared error of an AR spectral estimate is attained by the order selected for multistep prediction by the A/C Selection procedure and its alike when the underlying process is a nonzero mean infinite order not necessarily Gaussian A R process.