Electronic Journal of Statistics

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

Sévérien Nkurunziza and Kang Fu

Full-text: Open access

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.

Article information

Source
Electron. J. Statist., Volume 13, Number 1 (2019), 1400-1442.

Dates
Received: May 2018
First available in Project Euclid: 16 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1555380048

Digital Object Identifier
doi:10.1214/19-EJS1548

Mathematical Reviews number (MathSciNet)
MR3939302

Zentralblatt MATH identifier
07056155

Subjects
Primary: 62F30: Inference under constraints
Secondary: 62M02: Markov processes: hypothesis testing

Keywords
ADR change-point drift-parameter mean-reverting process Ornstein-Uhleneck process testing SDE shrinkage estimators unrestricted estimator

Rights
Creative Commons Attribution 4.0 International License.

Citation

Nkurunziza, Sévérien; Fu, Kang. Improved inference in generalized mean-reverting processes with multiple change-points. Electron. J. Statist. 13 (2019), no. 1, 1400--1442. doi:10.1214/19-EJS1548. https://projecteuclid.org/euclid.ejs/1555380048


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