On Efficient AR Spectral Estimation for Long-Range Predictions

ABSTRACT

This article discusses the concept of asymptotic efficiency 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 AIC selection procedure Akaike (1973 Akaike , H. ( 1973 ). Information theory and an extension of the maximum likelihood principle . In Petrov , B. N. , Csaki , F. eds. Proc. 2nd Int. Symp. on Information Theory. Budapest : Akademia Kiado , 267 – 281 . [Google Scholar]) and its alike when the underlying process is a non zero mean infinite order not necessarily Gaussian AR process.