On Hyperbolic Decay of Prediction Error Variance for Deterministic Stationary Sequences

One of the main problems in prediction theory of second-order stationary processes, called direct prediction problem, is to describe the asymptotic behavior of the best linear mean squared one-step ahead prediction error variance in predicting the value of a stationary process by the observed past of finite length as goes to infinity, depending on the regularity nature (deterministic or non-deterministic) of the underlying observed process . In this paper, we obtain sufficient conditions for hyperbolic decay of prediction error variance for deterministic stationary sequences, generalizing a result obtained by Rosenblatt [ 31 ].