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In this paper we suggest an extension of the forward search methodology to GARCH models which are often used for forecasting stock market volatility. It is frequently found that estimated residuals from GARCH models have excess kurtosis, even when one allows for conditional t-distributed errors. Some papers have appeared on outlier detection in GARCH models 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. 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. It is possible, through the forward search, to visualize the effect on estimated parameters of patches of extremal observations.

Analyzing Financial Time Series through Robust Estimators