Inference in a multivariate generalized mean-reverting process with a change-point
type: Item
instance of: scholarly article
title: Inference in a multivariate generalized mean-reverting process with a change-point
zbMATH Open document ID: 1441.62144
author: Sévérien Nkurunziza
author: Lei Shen
published in: Statistical Inference for Stochastic Processes
publication date: 2020-04-07T00:00:00Z
review text: From the authors' 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.'' The paper contains several results to analyze the maximum likelihood estimation problem for generalized multivariate Ornstein-Uhlenbeck processes. The models analyzed in this paper are able to capture seasonality (i.e., periodic components) and shocks (i.e., change-points) in a multivariate setting. Basic questions such as the computation of the maximum likelihood estimator, both restricted and unrestricted, are addressed, and their asymptotic normality is proved. The theoretical part is accompanied by a numerical study where the authors examine the performances of the maximum likelihood estimators in a \(4\)-dimensional stochastic process. The stochastic process is simulated via discretization and the results are presented in terms of the weighted squared error of each estimator.
reviewed by: Fabio Rapallo
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62M05
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 7186890
zbMATH Keywords: asymptotic normality
zbMATH Keywords: Brownian motion
zbMATH Keywords: change-point
zbMATH Keywords: drift-parameter
zbMATH Keywords: multivariate Ornstein-Uhlenbeck process
zbMATH Keywords: testing
zbMATH Keywords: SDE
zbMATH Keywords: shrinkage estimators
MaRDI profile type: Publication
full work available at URL: s11203-019-09204-1
OpenAlex ID: W2965828964
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DOI: 10.1007/S11203-019-09204-1
description: scientific article; zbMATH DE number 7186890