Abstract

Within the series of singular spectrum analysis (SSA) methods, there exist several versions of forecasting algorithms for signals corrupted by additive noise. In this paper, a technique is proposed to estimate the asymptotic accuracy of the recurrent version of such forecasting when the length of a series tends to infinity. Most elements of this construction can be reduced to already studied and published results, although some of them are hard to implement in specific situations. The article brings together all these elements and augments and comments on them. Several examples of determining estimates of accuracy for a recurrent forecast are given for specific signals and noises. The computational experiments carried out confirm the theoretical results.

中文翻译：

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奇异谱分析中循环预测精度的评述

摘要

在一系列奇异频谱分析 (SSA) 方法中，存在针对受加性噪声破坏的信号的多种预测算法版本。在本文中，提出了一种技术来估计当序列的长度趋于无穷大时这种预测的递归版本的渐近精度。这种结构的大多数元素都可以简化为已经研究和发表的结果，尽管其中一些在特定情况下很难实施。这篇文章汇集了所有这些元素，并对它们进行了补充和评论。针对特定信号和噪声，给出了确定周期性预测准确度估计值的几个示例。进行的计算实验证实了理论结果。