Weighted trimmed likelihood estimator for GARCH models

Generalized autoregressive heteroskedasticity (GARCH) models are widely used to reproduce stylized facts of financial time series and today play an essential role in risk management and volatility forecasting. But despite extensive research, problems are still encountered during parameter estimation in the presence of outliers. Here we show how this limitation can be overcome by applying the robust weighted trimmed likelihood estimator (WTLE) to the standard GARCH model. We suggest a fast implementation and explain how the additional robust parameter can be automatically estimated. We compare our approach with other recently introduced robust GARCH estimators and show through the results of an extensive simulation study that the proposed estimator provides robust and reliable estimates with a small computation cost. Moreover, the proposed fully automatic method for selecting the trimming parameter obviates the tedious fine tuning process required by other models to obtain a “robust” parameter, which may be appreciated by practitioners.