Sequential change point test in the presence of outliers: the density power divergence based approach

TL;DR

This paper introduces a robust sequential change point detection method using density power divergence, effective against outliers, applicable to i.i.d. and stationary time series, including GARCH models, with demonstrated validity through simulations and real data.

Contribution

It develops a new outlier-robust sequential change point detection procedure based on density power divergence, extending to time series and GARCH models.

Findings

Procedure is asymptotically valid for i.i.d. sequences.

Method maintains robustness in the presence of outliers.

Validated through simulations and real data applications.

Abstract

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.