On Hyperbolic Decay of Prediction Error Variance for Deterministic Stationary Sequences
Nikolay M. Babayan, Mamikon Smbatovich Ginovyan · Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) · 2020
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 $$X(0)$$ of a stationary process $$X(t)$$ by the observed past of finite length $$n$$ as $$n$$ goes to infinity, depending on the regularity nature (deterministic or non-deterministic) of the underlying observed process $$X(t)$$ . 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].