| Density forecasts, which embody a complete description of a forecaster' s view of the uncertainty concerning a variable's future value, are becoming increasingly commonplace. This dissertation is concerned with the evaluation of density forecasts. We study the properties of optimal density forecasts and propose a method for the evaluation of both univariate and multivariate density forecasts of data series that are based on these properties. This approach is applicable to data series with dynamic features. Furthermore, the method proposed is based on decision theoretic considerations and is especially appropriate in situations where the loss function is unknown. We also discuss how past forecast errors can be used to construct adjusted density forecasts that account for these errors. Other extensions discussed include evaluating h-step ahead forecasts, evaluating density forecasts under known loss functions and monitoring for structural change in the variable being forecast. Examples are used to illustrate the forecast evaluation procedure and the construction of adjusted density forecasts. These examples emphasize the density forecasting of conditionally heteroskedastic time series.; Several applications to empirical data are presented. An application of the univariate evaluation method to stock market returns produces evidence of structural change in the S&P 500 returns series. Adjusted forecasts which account for past forecast inadequacies are constructed and the improved properties of these forecasts are demonstrated. An application to inflation data suggests the non-optimality of forecasts by professional forecasters. Finally, the multivariate evaluation technique is applied to multivariate forecasts of exchange rates constructed with a Latent Factor GARCH model. An evaluation of these forecasts suggests possible improvements to this model. |
