Estimation and Testing in Multivariate Generalized Ornstein-Uhlenbeck Processes with Change-Points

Sévérien Nkurunziza ()
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Sévérien Nkurunziza: University of Windsor

Sankhya A: The Indian Journal of Statistics, 2023, vol. 85, issue 1, No 14, 400 pages

Abstract: Abstract In this paper, we consider an inference problem about the drift parameter matrix of multivariate generalized Ornstein-Uhlenbeck processes with multiple unknown change-points in the case where the drift parameter matrix is suspected to satisfy some restrictions. The established results generalize in six ways some recent findings about univariate generalized Ornstein-Uhlenbeck processes. First, we consider a multivariate process with multiple change-points. Second, we weaken the assumptions underlying some recent findings and we derive the unrestricted estimator (UE) and the restricted estimator (RE). Third, we derive the asymptotic property of the UE and the RE. Fourth, we construct a test for testing the hypothesized constraint. Fifth, we establish the asymptotic power of the derived test and we prove that it is consistent. Sixth, we derive a class of shrinkage estimators (SEs) and its asymptotic distributional risk.

Keywords: Asymptotic property; Drift-parameter matrix; James-Stein estimators; Multiple change-points; Multivariate mean-reverting; Testing; Shrinkage estimators; SDE; Wiener process.; Primary 62F30; Secondary 62M02 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13171-021-00251-6

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