Test for parameter change in the presence of outliers: the density power divergence based approach

This study considers the problem of testing for a parameter change in the presence of outliers. For this, we propose a robust test using the objective function of minimum density power divergence estimator (MDPDE) by Basu et al. (Biometrika, 1998), and then derive its limiting null distribution. Our test procedure can be readily extended to any parametric models in which MDPDE has been established. To illustrate this, we apply our test procedure to GARCH models. We demonstrate robust and efficient properties of the proposed test through simulation studies.