Pre-averaging fractional processes contaminated by noise, with an application to turbulence
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917199950643200 |
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| author | Chen, David Cheng, Yu Chong, Carsten Gentine, Pierre Jia, Wangdong Monier, Bryce Shen, Shiyang |
| author_facet | Chen, David Cheng, Yu Chong, Carsten Gentine, Pierre Jia, Wangdong Monier, Bryce Shen, Shiyang |
| contents | In this article, we consider the problem of estimating fractional processes based on noisy high-frequency data. Generalizing the idea of pre-averaging to a fractional setting, we exhibit a sequence of consistent estimators for the unknown parameters of interest by proving a law of large numbers for associated variation functionals. In contrast to the semimartingale setting, the optimal window size for pre-averaging depends on the unknown roughness parameter of the underlying process. We evaluate the performance of our estimators in a simulation study and use them to empirically verify Kolmogorov's 2/3-law in turbulence data contaminated by instrument noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_00867 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Pre-averaging fractional processes contaminated by noise, with an application to turbulence Chen, David Cheng, Yu Chong, Carsten Gentine, Pierre Jia, Wangdong Monier, Bryce Shen, Shiyang Statistics Theory Applications 60F25, 60G22, 62M09, 76M35, 62G05, 76F55 In this article, we consider the problem of estimating fractional processes based on noisy high-frequency data. Generalizing the idea of pre-averaging to a fractional setting, we exhibit a sequence of consistent estimators for the unknown parameters of interest by proving a law of large numbers for associated variation functionals. In contrast to the semimartingale setting, the optimal window size for pre-averaging depends on the unknown roughness parameter of the underlying process. We evaluate the performance of our estimators in a simulation study and use them to empirically verify Kolmogorov's 2/3-law in turbulence data contaminated by instrument noise. |
| title | Pre-averaging fractional processes contaminated by noise, with an application to turbulence |
| topic | Statistics Theory Applications 60F25, 60G22, 62M09, 76M35, 62G05, 76F55 |
| url | https://arxiv.org/abs/2212.00867 |