We cordially invite you to the

Ökonometrisches Forschungsseminar / Econometric Research Seminar (M. Deistler, A. Jumah, A. Weber)

on Thursday, May 10, 2001, at 9.15 a.m.

Institute for Advanced Studies, SZ VI, Stumpergasse 56, A-1060 Vienna

held by Gabriela DE RAAIJ and Burkhard RAUNIG (Österreichische Nationalbank)

"Evaluating Density Forecasts of Stock Market Returns"

Abstract: The paper deals with the evaluation of density forecasts, which have become quite popular in economics and finance. We use two probability integral transformations to evaluate such forecasts. The first transformation implies that the realizations transformed with respect to the forecasted densities of a stochastic process should be identically uniformly distributed if the density forecasts coincide with the densities underlying the true data generating process. The second transformation generates data that are identically normally distributed if the correct densities are forecasted. The second transformation enables us to apply standard statistical techniques to test for identically normally distributed data and hence for the quality of density forecasts. We use the methodology to evaluate density forecasts for daily returns of three stock market indices (S&P 500, DAX and ATX). Various models to forecast conditional densities are investigated. We consider the conditional normal distribution where the variances are estimated by moving averages or exponentially weighted moving averages, scaled t distributions and GARCH(1,1) variants with normally and t-distributed errors, respectively. In- and out-of-sample results for the density forecasting models are examined. Using the proposed methodology we find that GARCH models with t-distributed errors perform best in sample as well as out of sample. We are also able to demonstrate that certain misspecifications of a forecasting model are quite naturally reflected in the transformed series used for density forecast evaluation.

Key words: Density forecasting, Forecast evaluation, Risk management JEL Classification: G10, C52, C53

With best regards, Nina Gritzky **************************************************************************** Mag. Nina Gritzky IHS - Institut für Höhere Studien / Institute for Advanced Studies Stumpergasse 56 A-1060 Wien (Vienna), Austria

Tel: +43/1/59 991-145 Fax: +43/1/59 991-163 e-mail: gritzky@ihs.ac.at WWW: http://www.ihs.ac.at