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A Likelihood Ratio Approach to Sequential Change Point Detection for a General Class of Parameters

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.

Ketersediaan

Informasi Detail

Judul Seri

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION [JASA]; Vol.115 No.531 September 2020

No. Panggil

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Penerbit

: .,

Deskripsi Fisik

p. 1361 - 1377

Bahasa

English

ISBN/ISSN

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Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

-

Subjek

CHANGE POINT ANALYSIS
SELF-NORMALIZATION
LIKELIHOOD RATIO PRINCIPLE
SEQUENTIAL MONITORING

Info Detail Spesifik

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Pernyataan Tanggungjawab

Holger Dette, Josua Gosmann

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