A pseudo-likelihood estimator of the Ornstein-Uhlenbeck parameters from suprema observations
Résumé
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 density of the supremum. 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 these statistical tools to simulated and real data.
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