Asymptotic expansion of the drift estimator for the fractional Ornstein-Uhlenbeck process
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917629805985792 |
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| author | Tudor, Ciprian A. Yoshida, Nakahiro |
| author_facet | Tudor, Ciprian A. Yoshida, Nakahiro |
| contents | We present an asymptotic expansion formula of an estimator for the drift coefficient of the fractional Ornstein-Uhlenbeck process. As the machinery, we apply the general expansion scheme for Wiener functionals recently developed by the authors [26]. The central limit theorem in the principal part of the expansion has the classical scaling T^{1/2}. However, the asymptotic expansion formula is a complex in that the order of the correction term becomes the classical T^{-1/2} for H in (1/2,5/8), but T^{4H-3} for H in [5/8, 3/4). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_00967 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic expansion of the drift estimator for the fractional Ornstein-Uhlenbeck process Tudor, Ciprian A. Yoshida, Nakahiro Probability Methodology 62M09, 60F05, 62H12 We present an asymptotic expansion formula of an estimator for the drift coefficient of the fractional Ornstein-Uhlenbeck process. As the machinery, we apply the general expansion scheme for Wiener functionals recently developed by the authors [26]. The central limit theorem in the principal part of the expansion has the classical scaling T^{1/2}. However, the asymptotic expansion formula is a complex in that the order of the correction term becomes the classical T^{-1/2} for H in (1/2,5/8), but T^{4H-3} for H in [5/8, 3/4). |
| title | Asymptotic expansion of the drift estimator for the fractional Ornstein-Uhlenbeck process |
| topic | Probability Methodology 62M09, 60F05, 62H12 |
| url | https://arxiv.org/abs/2403.00967 |