Bootstrap prediction for returns and volatilities in GARCH models.

A new bootstrap procedure to obtain prediction densities of returns and volatilities of GARCH processes is proposed. Financial market participants have shown an increasing interest in prediction intervals as measures of uncertainty. Furthermore, accurate predictions of volatilities are critical for many financial models. The advantages of the proposed method are that it allows incorporation of parameter uncertainty and does not rely on distributional assumptions. The finite sample properties are analyzed by an extensive Monte Carlo simulation. Finally, the technique is applied to the Madrid Stock Market index, IBEX-35.Acknowledgements: We are very grateful for their helpful comments by three anonymous referees, the editor Stephen Pollock and seminar participants at the Universities of Valladolid, New South Wales and Canterbury and the June 2001 Time Series Workshop of Arrabida, the September 2001 International Conference on Modelling Volatility (Perth) and the June 2002 International Symposium on Forecasting (Dublin). We are also grateful to Gregorio Serna for providing the data set analyzed in this paper and to Dolores Redondas for helping us with the figures. Financial support was provided by projects DGES PB96-0111 and BEC2002-03720 from the Spanish Government and Cátedra de Calidad from BBVAPublicad