Maximum likelihood estimation in the ergodic Volterra Ornstein-Uhlenbeck process

2024/04/08 by Mohamed Ben Alaya, Martin Friesen, Alaya, Mohamed Ben +3
Engineering · Mathematics · #Control Systems and Identification #FOS: Mathematics #Probability (math.PR) #Statistical Methods and Inference #Statistical and numerical algorithms #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2404.05554

openalex publication_date 2024/04/08 · openalex created_date 2024/04/11 · openalex updated_date 2026/08/03

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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