Inference for Multiple Change-points in Piecewise Locally Stationary Time Series
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912826221658112 |
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| author | Ng, Wai Leong Tang, Xinyi Cheung, Mun Lau Gao, Jiacheng Yau, Chun Yip Dette, Holger |
| author_facet | Ng, Wai Leong Tang, Xinyi Cheung, Mun Lau Gao, Jiacheng Yau, Chun Yip Dette, Holger |
| contents | Change-point detection and locally stationary time series modeling are two major approaches for the analysis of non-stationary data. The former aims to identify stationary phases by detecting abrupt changes in the dynamics of a time series model, while the latter employs (locally) time-varying models to describe smooth changes in dependence structure of a time series. However, in some applications, abrupt and smooth changes can co-exist, and neither of the two approaches alone can model the data adequately. In this paper, we propose a novel likelihood-based procedure for the inference of multiple change-points in locally stationary time series. In contrast to traditional change-point analysis where an abrupt change occurs in a real-valued parameter, a change in locally stationary time series occurs in a parameter curve, and can be classified as a jump or a kink depending on whether the curve is discontinuous or not. We show that the proposed method can consistently estimate the number, locations, and the types of change-points. Two different asymptotic distributions corresponding respectively to jump and kink estimators are also established. Extensive simulation studies and a real data application to financial time series are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07400 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inference for Multiple Change-points in Piecewise Locally Stationary Time Series Ng, Wai Leong Tang, Xinyi Cheung, Mun Lau Gao, Jiacheng Yau, Chun Yip Dette, Holger Methodology Statistics Theory Change-point detection and locally stationary time series modeling are two major approaches for the analysis of non-stationary data. The former aims to identify stationary phases by detecting abrupt changes in the dynamics of a time series model, while the latter employs (locally) time-varying models to describe smooth changes in dependence structure of a time series. However, in some applications, abrupt and smooth changes can co-exist, and neither of the two approaches alone can model the data adequately. In this paper, we propose a novel likelihood-based procedure for the inference of multiple change-points in locally stationary time series. In contrast to traditional change-point analysis where an abrupt change occurs in a real-valued parameter, a change in locally stationary time series occurs in a parameter curve, and can be classified as a jump or a kink depending on whether the curve is discontinuous or not. We show that the proposed method can consistently estimate the number, locations, and the types of change-points. Two different asymptotic distributions corresponding respectively to jump and kink estimators are also established. Extensive simulation studies and a real data application to financial time series are provided. |
| title | Inference for Multiple Change-points in Piecewise Locally Stationary Time Series |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2601.07400 |