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

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.