Inference in Multivariate Generalized Ornstein-Uhlenbeck Processes with a Change-point

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 study the case where the matrix parameter satisfies uncertain restriction. Thus, we generalize some recent findings about univariate generalized Ornstein-Uhlenbeck processes. First, we establish a weaker condition for the existence of the unrestricted estimator (UE) and we derive the unrestricted estimator and the restricted estimator. Second, we establish the joint asymptotic normality of the unrestricted estimator and the restricted estimator under the sequence of local alternatives. Third, we construct a test for testing the uncertain restriction. The proposed test is also useful for testing the absence of the change-point. Fourth, we derive the asymptotic power of the proposed test and we prove that it is consistent. Fifth, we propose the shrinkage estimators and we prove that shrinkage estimators dominate the unrestricted estimator. Finally, in order to illustrate the performance of the proposed methods in short and medium period of observations, we conduct a simulation study which corroborate our theoretical findings.