Robust volatility forecasts and model selection in financial time series

In order to cope with the stylized facts of financial time series, many models have been proposed inside the GARCH family (e.g. EGARCH, GJR-GARCH, QGARCH, FIGARCH, LSTGARCH) and the stochastic volatility models (e.g. SV). Generally, all these models tend to produce very similar results as concerns forecasting performance. Most of the time it is difficult to choose which is the most appropriate specification. In addition, all these models are very sensitive to the presence of atypical observations. The purpose of this paper is to provide the user with new robust model selection procedures in financial models which downweight or eliminate the effect of atypical observations. The extreme case is when outliers are treated as missing data. In this paper we extend the theory of missing data to the family of GARCH models and show how to robustify the loglikelihood to make it insensitive to the presence of outliers. The suggested procedure enables us both to detect atypical observations and to select the best models in terms of forecasting performance.