Inference in a multivariate generalized mean-reverting process with a change-point (Q1984652)

From the authors' abstract: ``In this paper, we study inference problem about the drift parameter matrix in multivariate generalized Ornstein-Uhlenbeck processes with an unknown change-point. In particular, we consider the case where the parameter matrix may satisfy some restrictions. Thus, we generalize in five ways some recent findings about univariate generalized Ornstein-Uhlenbeck processes.'' The paper contains several results to analyze the maximum likelihood estimation problem for generalized multivariate Ornstein-Uhlenbeck processes. The models analyzed in this paper are able to capture seasonality (i.e., periodic components) and shocks (i.e., change-points) in a multivariate setting. Basic questions such as the computation of the maximum likelihood estimator, both restricted and unrestricted, are addressed, and their asymptotic normality is proved. The theoretical part is accompanied by a numerical study where the authors examine the performances of the maximum likelihood estimators in a \(4\)-dimensional stochastic process. The stochastic process is simulated via discretization and the results are presented in terms of the weighted squared error of each estimator.