ON RISSANEN'S LOWER BOUND ON THE ACCUMULATED MEAN-SQUARE PREDICTION ERROR

Abstract. Rissanen (1984) presents a lower bound on the accumulated mean square prediction error for a Gaussian ARMA process. Rissanen proves this result using coding theory. In this paper we show that this bound is related to the Cramer-Rao bound and Fisher's bound on asymptotic variances, for the case of a Gaussian AR process. This provides some insight into Rissanen's lower bound. Analogues of Rissanen's bound, for nonaccumulated prediction error and a Gaussian AR process, are also presented and discussed.