Change-Point Detection in Autoregressive Models with no Moment Assumptions

Fumiya Akashi, Holger Dette*, Yan Liu


研究成果: Article査読

2 被引用数 (Scopus)


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.

ジャーナルJournal of Time Series Analysis
出版ステータスPublished - 2018 9月

ASJC Scopus subject areas

  • 統計学および確率
  • 統計学、確率および不確実性
  • 応用数学


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