Maximum likelihood estimation in the ergodic Volterra Ornstein-Uhlenbeck process
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909811018301440 |
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| author | Alaya, Mohamed Ben Friesen, Martin Kremer, Jonas |
| author_facet | Alaya, Mohamed Ben Friesen, Martin Kremer, Jonas |
| contents | We study statistical inference of the drift parameters for the Volterra Ornstein-Uhlenbeck process on R in the ergodic regime. For continuous-time observations, we derive the corresponding maximum likelihood estimators and show that they are strongly consistent and asymptotically normal locally uniformly in the parameters. For the case of discrete high-frequency observations, we prove similar results by discretization of the continuous-time maximum likelihood estimator. Finally, for discrete low-frequency observations, we show that the method of moments is consistent. Our proofs are crucially based on the law of large numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05554 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximum likelihood estimation in the ergodic Volterra Ornstein-Uhlenbeck process Alaya, Mohamed Ben Friesen, Martin Kremer, Jonas Statistics Theory Probability We study statistical inference of the drift parameters for the Volterra Ornstein-Uhlenbeck process on R in the ergodic regime. For continuous-time observations, we derive the corresponding maximum likelihood estimators and show that they are strongly consistent and asymptotically normal locally uniformly in the parameters. For the case of discrete high-frequency observations, we prove similar results by discretization of the continuous-time maximum likelihood estimator. Finally, for discrete low-frequency observations, we show that the method of moments is consistent. Our proofs are crucially based on the law of large numbers. |
| title | Maximum likelihood estimation in the ergodic Volterra Ornstein-Uhlenbeck process |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2404.05554 |