Least squares estimation of a shift in linear processes

Jushan Bai

MPRA Paper from University Library of Munich, Germany

Abstract: This paper considers a mean shift with an unknown shift point in a linear process and estimates the unknown shift point (change point) by the method of least squares. Pre-shift and post-shift means are estimated concurrently with the change point. The consistency and the rate of convergence for the estimated change point are established. The asymptotic distribution for the change point estimator is obtained when the magnitude of shift is small. It is shown that serial correlation affects the variance of the change point estimator via the sum of the coefficients (impulses) of the linear process. When the underlying process is an ARMA, a mean shift causes overestimation of its order. A simple procedure is suggested to mitigate the bias in order estimation.

Keywords: Mean shift; linear processes; change point; rate of convergence; order estimation; generalized residuals (search for similar items in EconPapers)
JEL-codes: C13 C22 (search for similar items in EconPapers)
Date: 1993-02-16
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Published in Journal of Time Series Analysis 5.15(1994): pp. 453-472

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/32878/1/MPRA_paper_32878.pdf original version (application/pdf)

Related works:
Journal Article: LEAST SQUARES ESTIMATION OF A SHIFT IN LINEAR PROCESSES (1994)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:32878

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().