Change-Point Detection in Autoregressive Models with no Moment Assumptions

Fumiya Akashi, Holger Dette, Yan Liu

Research output: Contribution to journalArticle

Abstract

In this paper we consider the problem of detecting a change in the parameters of an autoregressive process where the moments of the innovation process do not necessarily exist. An empirical likelihood ratio test for the existence of a change point is proposed and its asymptotic properties are studied. In contrast to other works on change-point tests using empirical likelihood, we do not assume knowledge of the location of the change point. In particular, we prove that the maximizer of the empirical likelihood is a consistent estimator for the parameters of the autoregressive model in the case of no change point and derive the limiting distribution of the corresponding test statistic under the null hypothesis. We also establish consistency of the new test. A nice feature of the method is the fact that the resulting test is asymptotically distribution-free and does not require an estimate of the long-run variance. The asymptotic properties of the test are investigated by means of a small simulation study, which demonstrates good finite-sample properties of the proposed method.

Original languageEnglish
Pages (from-to)763-786
Number of pages24
JournalJournal of Time Series Analysis
Volume39
Issue number5
DOIs
Publication statusPublished - 2018 Sep 1

Fingerprint

Change-point Detection
Change Point
Autoregressive Model
Empirical Likelihood
Innovation
Statistics
Moment
Asymptotic Properties
Consistent Estimator
Distribution-free
Autoregressive Process
Likelihood Ratio Test
Long-run
Limiting Distribution
Null hypothesis
Test Statistic
Simulation Study
Change point
Autoregressive model
Estimate

Keywords

  • autoregressive processes
  • change-point analysis
  • Empirical likelihood
  • infinite variance

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

Change-Point Detection in Autoregressive Models with no Moment Assumptions. / Akashi, Fumiya; Dette, Holger; Liu, Yan.

In: Journal of Time Series Analysis, Vol. 39, No. 5, 01.09.2018, p. 763-786.

Research output: Contribution to journalArticle

Akashi, Fumiya ; Dette, Holger ; Liu, Yan. / Change-Point Detection in Autoregressive Models with no Moment Assumptions. In: Journal of Time Series Analysis. 2018 ; Vol. 39, No. 5. pp. 763-786.
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