Least‐squares Estimation of an Unknown Number of Shifts in a Time Series

Marc Lavielle and Eric Moulines

Journal of Time Series Analysis, 2000, vol. 21, issue 1, 33-59

Abstract: In this contribution, general results on the off‐line least‐squares estimate of changes in the mean of a random process are presented. First, a generalisation of the Hajek‐Renyi inequality, dealing with the fluctuations of the normalized partial sums, is given. This preliminary result is then used to derive the consistency and the rate of convergence of the change‐points estimate, in the situation where the number of changes is known. Strong consistency is obtained under some mixing conditions. The limiting distribution is also computed under an invariance principle. The case where the number of changes is unknown is then addressed. All these results apply to a large class of dependent processes, including strongly mixing and also long‐range dependent processes.

Date: 2000
References: Add references at CitEc
Citations: View citations in EconPapers (90)

Downloads: (external link)
https://doi.org/10.1111/1467-9892.00172

Related works:
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:bla:jtsera:v:21:y:2000:i:1:p:33-59

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0143-9782

Access Statistics for this article

Journal of Time Series Analysis is currently edited by M.B. Priestley

More articles in Journal of Time Series Analysis from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().