Estimation and testing in generalized mean-reverting processes with change-point

Sévérien Nkurunziza () and Pei Patrick Zhang ()
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Sévérien Nkurunziza: University of Windsor
Pei Patrick Zhang: University of Windsor

Statistical Inference for Stochastic Processes, 2018, vol. 21, issue 1, No 8, 215 pages

Abstract: Abstract In this paper, we study an inference problem in generalized Ornstein–Uhlenbeck processes with an unknown change-point when the drift parameter is suspected to satisfy a linear restriction. The testing problem studied generalizes a very recent problem about testing the existence of a change-point. To this end, we derive the asymptotic properties of the unrestricted estimator (UE) and the restricted estimator for the drift parameters, and we construct some shrinkage estimators (SEs). Further, we derive a test for testing the uncertain restriction and establish its asymptotic power. Moreover, we derive the asymptotic distributional risk of the proposed estimators and we prove that SEs dominate the UE. Finally, we present some numerical results which confirm the consistency of the proposed test as well as the superiority of the SEs over UE.

Keywords: ADR; Change-point; Drift-parameter; Mean-reverting process; Ornstein–Uhleneck process; Testing; SDE; Shrinkage estimators; Unrestricted estimator (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11203-016-9151-3

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