Quasi-Likelihood Estimation for Ornstein-Uhlenbeck Diffusion Observed at Random Time Points

Abstract

In this paper, we study the quasi-likelihood estimator of the drift parameter θ in the Ornstein-Uhlenbeck diffusion process, when the process is observed at random time points, which are assumed to be unobservable. These time points are arrival times of a Poisson process with known rate. The asymptotic properties of the quasi-likelihood estimator (QLE) of θ, as well as those of its approximations are also elucidated. An extensive simulation study of these estimators is also performed. As a corollary to this work, we obtain the quasi-likelihood estimator iteratively in the deterministic framework with non-equidistant time points.