A Wide-Sense Stationarity Test Based on the Geometric Structure of Covariance

Fuente: arXiv
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Main Authors: Wang, Yinbu, Xu, Yong
Format: Preprint
Published: 2025
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author Wang, Yinbu
Xu, Yong
author_facet Wang, Yinbu
Xu, Yong
contents This paper presents a test for wide-sense stationarity (WSS) based on the geometry of the covariance function. We estimate local patches of the covariance surface and then check whether the directional derivative in the $(1,1,0)$ direction is zero on each patch. The method only requires the covariance function to be locally smooth and does not assume stationarity in advance. It can be applied to general stochastic dynamical systems and provides a time-resolved view. We apply the test method to an SDOF system and to a stochastic Duffing oscillator. These examples show that the method is numerically stable and can detect departures from WSS in practice.
format Preprint
id arxiv_https___arxiv_org_abs_2512_23251
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Wide-Sense Stationarity Test Based on the Geometric Structure of Covariance
Wang, Yinbu
Xu, Yong
Methodology
Data Analysis, Statistics and Probability
60G10(Primary), 62M10(Secondary), 37M10
This paper presents a test for wide-sense stationarity (WSS) based on the geometry of the covariance function. We estimate local patches of the covariance surface and then check whether the directional derivative in the $(1,1,0)$ direction is zero on each patch. The method only requires the covariance function to be locally smooth and does not assume stationarity in advance. It can be applied to general stochastic dynamical systems and provides a time-resolved view. We apply the test method to an SDOF system and to a stochastic Duffing oscillator. These examples show that the method is numerically stable and can detect departures from WSS in practice.
title A Wide-Sense Stationarity Test Based on the Geometric Structure of Covariance
topic Methodology
Data Analysis, Statistics and Probability
60G10(Primary), 62M10(Secondary), 37M10
url https://arxiv.org/abs/2512.23251