论文标题
固定序列的预测误差的渐近行为
Asymptotic behavior of the prediction error for stationary sequences
论文作者
论文摘要
离散时间二阶固定过程$ x（t）$的预测理论的主要问题之一是将最佳线性平均值预测错误的渐近行为描述在预测$ x（0）$给定$ x（t），$ x（t），$ -n \ le t \ le-t \ le-1 $中，为$ n $。这种行为取决于规律性（确定性或非确定性）以及基础观察到的过程$ x（t）$的依赖性结构。在本文中，我们考虑了确定性和非确定过程的这个问题，并调查了一些最新结果。我们专注于较少研究的案例 - 确定性过程。事实证明，对于非确定过程，预测误差的渐近行为取决于观察到的过程$ x（t）$的依赖性结构以及其光谱密度$ f $的差异属性，而对于确定性过程，它是由$ x（t）$ x（t）$和signulariument ossed supspralities of Spectralitival of Spectral dymulartival of Spectral d $ f $ f $ f $ f $ f $ f的。
One of the main problem in prediction theory of discrete-time second-order stationary processes $X(t)$ is to describe the asymptotic behavior of the best linear mean squared prediction error in predicting $X(0)$ given $ X(t),$ $-n\le t\le-1$, as $n$ goes to infinity. This behavior depends on the regularity (deterministic or nondeterministic) and on the dependence structure of the underlying observed process $X(t)$. In this paper we consider this problem both for deterministic and nondeterministic processes and survey some recent results. We focus on the less investigated case - deterministic processes. It turns out that for nondeterministic processes the asymptotic behavior of the prediction error is determined by the dependence structure of the observed process $X(t)$ and the differential properties of its spectral density $f$, while for deterministic processes it is determined by the geometric properties of the spectrum of $X(t)$ and singularities of its spectral density $f$.
