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

This study considers the problem of testing for parameter change, particularly in the presence of outliers. To lessen the impact of outliers, we propose a robust test based on the density power divergence introduced by Basu et al. (Biometrika, 1998), and then derive its limiting null distribution. Our test procedure can be naturally extended to any parametric model to which MDPDE can be applied. To illustrate this, we apply our test procedure to GARCH models. We demonstrate the validity and robustness of the proposed test through a simulation study. In a real data application to the Hang Seng index, our test locates some change-points that are not detected by the existing tests such as the score test and the residual-based CUSUM test.