A Likelihood Ratio Approach to Sequential Change Point Detection for a General Class of Parameters. Issue 531 (2nd July 2020)

• Record Type: Journal Article
• Authors: Dette, Holger; Gösmann, Josua
• Is Part Of: Journal of the American Statistical Association. Volume 115:Issue 531(2020)
• Page Start: 1361
• Page End: 1377
• Publication Date: 2020-07-02
• Subjects: Change point analysis -- Likelihood ratio principle -- Self-normalization -- Sequential monitoring; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2019.1630562
• Languages: English
• ISSNs: 0162-1459

Abstract

Abstract: In this article, we propose a new approach for sequential monitoring of a general class of parameters of a d -dimensional time series, which can be estimated by approximately linear functionals of the empirical distribution function. We consider a closed-end method, which is motivated by the likelihood ratio test principle and compare the new method with two alternative procedures. We also incorporate self-normalization such that estimation of the long-run variance is not necessary. We prove that for a large class of testing problems the new detection scheme has asymptotic level α and is consistent. The asymptotic theory is illustrated for the important cases of monitoring a change in the mean, variance, and correlation. By means of a simulation study it is demonstrated that the new test performs better than the currently available procedures for these problems. Finally, the methodology is illustrated by a small data example investigating index prices from the dot-com bubble. Supplementary materials for this article are available online.