Robustifying GARCH models through the forward search

In this paper we suggest an extension of the forward search methodology to GARCH models which are often used for forecasting stock market volatility. In the case of GARCH models outliers are strictly related to extreme observations which are responsible for the well-known volatility clustering of financial returns. Some papers have appeared on outlier detection in GARCH models (see, for example, [3]) but the proposed methods are iterative and may suffer from masking effects. The forward search is a method for determining the effect of outliers on fitted parameters and for detecting also masked outliers. Through the forward search, it is also possible to visualize the effect on estimated parameters of patches of extremal observations.