A Wide-Sense Stationarity Test Based on the Geometric Structure of Covariance
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909996336283648 |
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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 |
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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 |