Maximum likelihood estimation in the ergodic Volterra Ornstein-Uhlenbeck process

Mohamed Ben Alaya; Martin Friesen; Jonas Kremer

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arXiv · 2404.05554

Maximum likelihood estimation in the ergodic Volterra Ornstein-Uhlenbeck process

Mohamed Ben Alaya·Martin Friesen·Jonas Kremer

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Abstract

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.

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BibTeX RIS

Mohamed Ben Alaya, Martin Friesen, Jonas Kremer. 2024-04-08. Maximum likelihood estimation in the ergodic Volterra Ornstein-Uhlenbeck process. https://arxiv.org/abs/2404.05554

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