Gaussian Approximation For Non-stationary Time Series with Optimal Rate and Explicit Construction
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916349349986304 |
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| author | Bonnerjee, Soham Karmakar, Sayar Wu, Wei Biao |
| author_facet | Bonnerjee, Soham Karmakar, Sayar Wu, Wei Biao |
| contents | Statistical inference for time series such as curve estimation for time-varying models or testing for existence of change-point have garnered significant attention. However, these works are generally restricted to the assumption of independence and/or stationarity at its best. The main obstacle is that the existing Gaussian approximation results for non-stationary processes only provide an existential proof and thus they are difficult to apply. In this paper, we provide two clear paths to construct such a Gaussian approximation for non-stationary series. While the first one is theoretically more natural, the second one is practically implementable. Our Gaussian approximation results are applicable for a very large class of non-stationary time series, obtain optimal rates and yet have good applicability. Building on such approximations, we also show theoretical results for change-point detection and simultaneous inference in presence of non-stationary errors. Finally we substantiate our theoretical results with simulation studies and real data analysis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_02913 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gaussian Approximation For Non-stationary Time Series with Optimal Rate and Explicit Construction Bonnerjee, Soham Karmakar, Sayar Wu, Wei Biao Statistics Theory Statistical inference for time series such as curve estimation for time-varying models or testing for existence of change-point have garnered significant attention. However, these works are generally restricted to the assumption of independence and/or stationarity at its best. The main obstacle is that the existing Gaussian approximation results for non-stationary processes only provide an existential proof and thus they are difficult to apply. In this paper, we provide two clear paths to construct such a Gaussian approximation for non-stationary series. While the first one is theoretically more natural, the second one is practically implementable. Our Gaussian approximation results are applicable for a very large class of non-stationary time series, obtain optimal rates and yet have good applicability. Building on such approximations, we also show theoretical results for change-point detection and simultaneous inference in presence of non-stationary errors. Finally we substantiate our theoretical results with simulation studies and real data analysis. |
| title | Gaussian Approximation For Non-stationary Time Series with Optimal Rate and Explicit Construction |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2408.02913 |