Forecasting volatility in GARCH models with additive outliers

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Acknowledgement

The authors gratefully acknowledge the helpful observations and suggestions of two anonymous referees. This article is part of a research project financed by the Spanish Ministry of Education and Science and Feder (SEJ2006-02328).

Notes

†Chan and McAleer (2002) propose a specification of STAR models with GARCH errors that opens interesting research lines. However, these exceed the objective of this note.

‡The attention given to the effects of outliers in linear time series models (ARMA models) has been much more extensive (see, e.g. Hillmer 1984, Ledolter 1989, Chen and Liu 1993, Wu et al. 1993, Trívez 1995, Phillips 1996)

†The criterion of taking a quadratic loss function can give rise to spurious estimations in the presence of outliers, so that the absolute mean error is more appropriate, being inherently robust

†All the experiments have been carried out using the GAUSS computer program with programming developed by the authors of this note.

‡The estimation method employed is that of maximum likelihood, more specifically, applying the algorithm developed by Berndt etal. (1974).