Change point detection with stable AR(1) errors

Alina Bazarova*, István Berkes, Lajos Horváth

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review


In this paper we develop two types of tests to detect changes in the location parameters of dependent observations with infinite variances. We consider the case of autoregressive processes of order one with independent innovations in the domain of attraction of a stable law. If the d largest (in magnitude) observations are removed from the sample, then the standard CUSUM process developed for weakly dependent observations with finite variance can be used assuming that 𝑑=𝑑(𝑛)→∞ and d(n)∕n → 0 as n, the sample size, tends to ∞. We study two types of statistics. In case of the maximally selected CUSUM process we estimate the long run variance by kernel estimators and we develop the corresponding change point test. We also propose ratio statistics which do not depend on the long run variances. Monte Carlo simulations illustrate that the limit results can be used even in case of small and moderate sample sizes.
Original languageEnglish
Title of host publicationAsymptotic Laws and Methods in Stochastics
ISBN (Print)978-1-4939-3075-3
Publication statusPublished - 2015
EventAsymptotic methods in stochastics - Miklós Csörgő is 85 - Ottawa, Canada
Duration: 9 Jul 201314 Jul 2013

Publication series

NameFields Institute Communications


ConferenceAsymptotic methods in stochastics - Miklós Csörgő is 85

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)


Dive into the research topics of 'Change point detection with stable AR(1) errors'. Together they form a unique fingerprint.

Cite this