基于重对数律的非平稳性度量

摘要/Abstract

摘要：

时间序列的非平稳性与很多领域的应用密切相关. 如何衡量时间序列的非平稳程度是一个重要的研究课题, 已经构建了一个完整的非平稳性度量框架, 其中稳定集合的判别标准处于核心地位. 该文基于独立同分布随机变量的重对数律, 提出了一种新的稳定集合判别标准, 与已有标准相比, 在显著性水平相同的情况下, 收敛标准更为严格, 且所需的参数更少, 该方法提高了非平稳性度量在 NS 较小时的分辨率. 对于确定性信号的参数校准, 新方法得到的结果更为精确.

关键词: 非平稳性度量, 稳定集合, 重对数律

Abstract:

The non-stationarity of time series is closely related to its application in many fields. How to measure the non-stationarity of time series is an important research topic. A complete non-stationarity measurement framework has been constructed, in which the criterion of stable set is the core. In this paper, based on the law of iterated logarithm of independent identically distributed random variables, a new criterion of stable set is proposed. Compared with the existing criterion, the convergence criterion is more strict and requires fewer parameters when the level of significance is the same. This method improves the resolution of non-stationary measurement when NS is small. For the parameter calibration of deterministic signals, the new method can get more accurate results.

Key words: Non-stationary measure, Stable set, Law of the iterated logarithm

中图分类号:

O211

张聪, 丁义明. 基于重对数律的非平稳性度量[J]. 数学物理学报, 2023, 43(6): 1855-1868.

Zhang Cong, Ding Yiming. Non-stationarity Measurement Based on Law of Iterated Logarithm[J]. Acta mathematica scientia,Series A, 2023, 43(6): 1855-1868.

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