Robust maximum entropy test for GARCH models based on a minimum density power divergence estimator

The maximum entropy test, as designed for examining goodness-of-fit with a non-robust estimator such as the maximum likelihood estimator, can suffer from severe size distortions when the data are contaminated by outliers. The objective of this study is to develop a robust maximum entropy test for the normality of GARCH models. We construct the test statistic based on the minimum density power divergence estimator and verify its limiting null distribution. A bootstrap method is also discussed, and its performance is evaluated through simulations. According to the simulation results, the proposed test can successfully achieve reasonable sizes in the presence of outliers.