A pseudo-likelihood estimator of the Ornstein–Uhlenbeck parameters from suprema observations

Christophette Blanchet-Scalliet (), Diana Dorobantu () and Benoit Nieto ()
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Christophette Blanchet-Scalliet: Universite Claude Bernard Lyon 1, Université Jean Monnet
Diana Dorobantu: Université Claude Bernard Lyon 1
Benoit Nieto: Universite Claude Bernard Lyon 1, Université Jean Monnet

Statistical Inference for Stochastic Processes, 2024, vol. 27, issue 2, No 6, 407-425

Abstract: Abstract In this paper, we propose an estimator for the Ornstein–Uhlenbeck parameters based on observations of its supremum. We derive an analytic expression for the supremum density. Making use of the pseudo-likelihood method based on the supremum density, our estimator is constructed as the maximal argument of this function. Using weak-dependency results, we prove some statistical properties on the estimator such as consistency and asymptotic normality. Finally, we apply our estimator to simulated and real data.

Keywords: Ornstein–Uhlenbeck process; Supremum law; Parameters estimation; Asymptotic normality (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11203-024-09307-4

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