Estimation of all parameters in the reflected Orntein-Uhlenbeck process from discrete observations

TL;DR

This paper develops consistent and asymptotically normal estimators for all parameters of a reflected Ornstein-Uhlenbeck process based on discrete observations, solving an open problem in the field.

Contribution

It introduces generalized moment estimators for all parameters of the reflected Ornstein-Uhlenbeck process and proves their strong consistency and asymptotic normality.

Findings

Estimators are strongly consistent as sample size increases.

Estimators are asymptotically normal.

Provides a complete solution to parameter estimation in reflected Ornstein-Uhlenbeck processes.

Abstract

Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling time step h > 0 arbitrarily fixed, we prove the strong consistency and asymptotic normality of our estimators as the sampling size n tends to infinity. This provides a complete solution to an open problem left in Hu et al. [5].