Least squares estimation for reflected Ornstein-Uhlenbeck processes with one and two sided barriers

Abstract

Diffusion processes for modelling, among others, dataset for instance, (macro-) econometrics, mathematical finance, biology, queueing, and electrical engineering often involve reflecting one or two barriers. In this paper, we investigate the least squares estimation $\left(LSE\right)$ for a one dimensional continuous-time ergodic reflected Ornstein-Uhlenbeck $(ROU)$ processes that returns continuously and immediately to the interior of the state space when it attains one and/or two-sided barriers. Both the estimates based on continuously observed processes and discretely observed processes are considered. So, we derive explicit formulas for the estimates, and then we establish their consistency and asymptotic normality ($CAN$). We also illustrate the $CAN$ properties of the estimates through a Monte Carlo simulation and comparing with respect to maximum likelihood estimation ($LME$) as benchmark method showing the performance of the proposed estimators withmoderate sample sizes. The method is valid irrespective of the length of the time intervals between consecutive observations.