Parameter estimation with exact distribution for multidimensional Ornstein-Uhlenbeck processes

Abstract

It is shown that the suitably normalized maximum likelihood estimators of some parameters of multidimensional Ornstein-Uhlenbeck processes with coefficient matrix of a special structure have exactly a normal distribution. This result provides a generalization to an arbitrary dimension of the well-known behavior of the estimator of the period of a complex AR(1) process. © 1996 Academic Press, Inc.