Open Access
2021 Sequential change point test in the presence of outliers: the density power divergence based approach
Junmo Song
Author Affiliations +
Electron. J. Statist. 15(1): 3504-3550 (2021). DOI: 10.1214/21-EJS1868


In this study, we consider a problem of monitoring parameter changes particularly in the presence of outliers. To propose a sequential procedure that is robust against outliers, we use the density power divergence to derive a detector and stopping time that make up our procedure. We first investigate the asymptotic properties of our sequential procedure for i.i.d. sequences and then extend the proposed procedure to stationary time series models, where we provide a set of sufficient conditions under which the proposed procedure has an asymptotically controlled size and consistency in power. As an application, our procedure is applied to the GARCH models. We demonstrate the validity and robustness of the proposed procedure through a simulation study. Finally, two real data analyses are provided to illustrate the usefulness of the proposed sequential procedure.

Funding Statement

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2019R1I1A3A01056924).


The author would like to thank the associate editor for carefully examining the paper and providing valuable comments.


Download Citation

Junmo Song. "Sequential change point test in the presence of outliers: the density power divergence based approach." Electron. J. Statist. 15 (1) 3504 - 3550, 2021.


Received: 1 December 2020; Published: 2021
First available in Project Euclid: 7 July 2021

arXiv: 2008.02365
Digital Object Identifier: 10.1214/21-EJS1868

Primary: 62F35 , 62L10
Secondary: 62M10

Keywords: Density power divergence , GARCH models , monitoring parameter change , Outliers , robust test , Sequential change detection , time series

Vol.15 • No. 1 • 2021
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