Trend estimation for time series with polynomial-tailed noise
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909489494491136 |
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| author | Neumann, Michael H. Leucht, Anne |
| author_facet | Neumann, Michael H. Leucht, Anne |
| contents | For time series data observed at non-random and possibly non-equidistant time points, we estimate the trend function nonparametrically. Under the assumption of a bounded total variation of the function and low-order moment conditions on the errors we propose a nonlinear wavelet estimator which uses a Haar-type basis adapted to a possibly non-dyadic sample size. An appropriate thresholding scheme for sparse signals with an additive polynomial-tailed noise is first derived in an abstract framework and then applied to the problem of trend estimation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08280 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trend estimation for time series with polynomial-tailed noise Neumann, Michael H. Leucht, Anne Statistics Theory For time series data observed at non-random and possibly non-equidistant time points, we estimate the trend function nonparametrically. Under the assumption of a bounded total variation of the function and low-order moment conditions on the errors we propose a nonlinear wavelet estimator which uses a Haar-type basis adapted to a possibly non-dyadic sample size. An appropriate thresholding scheme for sparse signals with an additive polynomial-tailed noise is first derived in an abstract framework and then applied to the problem of trend estimation. |
| title | Trend estimation for time series with polynomial-tailed noise |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2502.08280 |