Improved inference in generalized mean-reverting processes with multiple change-points

Abstract

In this paper, we consider inference problem about the drift parameter vector in generalized mean reverting processes with multiple and unknown change-points. In particular, we study the case where the parameter may satisfy uncertain restriction. As compared to the results in literature, we generalize some findings in five ways. First, we consider the model which incorporates the uncertain prior knowledge. Second, we derive the unrestricted estimator (UE) and the restricted estimator (RE) and we study their asymptotic properties. Third, we derive a test for testing the hypothesized restriction and we derive its asymptotic local power. We also prove that the proposed test is consistent. Fourth, we construct a class of shrinkage type estimators (SEs) which encloses the UE, the RE and classical SEs. Fifth, we derive the relative risk dominance of the proposed estimators. More precisely, we prove that the SEs dominate the UE. Finally, we present some simulation results which corroborate the established theoretical findings.