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

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. First, the target parameter is a matrix and we derive a sufficient condition for the existence of the unrestricted estimator (UE) and the restricted estimator (RE). Second, we establish the joint asymptotic normality of the UE and the RE under a collection 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 (SEs) and we prove that SEs dominate the UE. Finally, we conduct some simulation studies which corroborate our theoretical findings.