Lévy Area Analysis and Parameter Estimation for fOU Processes via Non-Geometric Rough Path Theory
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2018
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| _version_ | 1866909296050044928 |
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| author | Qian, Zhongmin Xu, Xingcheng |
| author_facet | Qian, Zhongmin Xu, Xingcheng |
| contents | This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting. To tackle this problem, we propose a novel approach based on rough path theory that allows us to construct pathwise rough path estimators from both continuous and discrete observations of a single path. Our approach is particularly suitable for high-frequency data. To formulate the parameter estimators, we introduce a theory of pathwise Itô integrals with respect to fractional Brownian motion. By establishing the regularity of fractional Ornstein-Uhlenbeck processes and analyzing the long-term behavior of the associated Lévy area processes, we demonstrate that our estimators are strongly consistent and pathwise stable. Our findings offer a new perspective on estimating the drift parameter matrix for fractional Ornstein-Uhlenbeck processes in multi-dimensional settings, and may have practical implications for fields including finance, economics, and engineering. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_11039 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Lévy Area Analysis and Parameter Estimation for fOU Processes via Non-Geometric Rough Path Theory Qian, Zhongmin Xu, Xingcheng Probability Statistics Theory 60H05, 62F12, 62M09, 91G30 This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting. To tackle this problem, we propose a novel approach based on rough path theory that allows us to construct pathwise rough path estimators from both continuous and discrete observations of a single path. Our approach is particularly suitable for high-frequency data. To formulate the parameter estimators, we introduce a theory of pathwise Itô integrals with respect to fractional Brownian motion. By establishing the regularity of fractional Ornstein-Uhlenbeck processes and analyzing the long-term behavior of the associated Lévy area processes, we demonstrate that our estimators are strongly consistent and pathwise stable. Our findings offer a new perspective on estimating the drift parameter matrix for fractional Ornstein-Uhlenbeck processes in multi-dimensional settings, and may have practical implications for fields including finance, economics, and engineering. |
| title | Lévy Area Analysis and Parameter Estimation for fOU Processes via Non-Geometric Rough Path Theory |
| topic | Probability Statistics Theory 60H05, 62F12, 62M09, 91G30 |
| url | https://arxiv.org/abs/1803.11039 |