Abstract

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].

中文翻译：

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确定性平稳序列的预测误差方差的双曲线衰减

摘要

二阶平稳过程预测理论中的主要问题之一，被称为直接预测问题，是描述在预测值\（X（0）\时）最佳线性均方提前一步预测误差方差的渐近行为。）固定处理的\（X（t）的\）由有限长度的所观察到的过去\（N \）作为\（N \）趋于无穷大，这取决于规律性性质（确定性或非确定性）的底层的观察到的过程\（X（t）\）。在本文中，我们为确定性平稳序列获得了预测误差方差的双曲线衰减的充分条件，并推广了Rosenblatt [31]得出的结果。