Density forecasting: a survey

Abstract

A density forecast of the realization of a random variable at some future time is an estimate of the probability distribution of the possible future values of that variable. This article presents a selective survey of applications of density forecasting in macroeconomics and finance, and discusses some issues concerning the production, presentation, and evaluation of density forecasts. Copyright © 2000 John Wiley & Sons, Ltd.

The Out-of-Sample Success of Term Structure Models as Exchange Rate Predictors: A Step Beyond

“…With regard to the evaluation of forecasting models, although the relevant literature has traditionally focused on accuracy evaluations based on point forecasts, several authors have recently emphasized the importance of evaluating the forecast accuracy of economic models on the basis of density -as opposed to point -forecasting performance (see, inter alia, Diebold, Gunther and Tay, 1998;Granger and Pesaran, 1999;Tay and Wallis, 2000;Timmerman, 2000;Pesaran and Skouras, 2001). Especially when evaluating nonlinear models, which are capable of producing highly non-normal forecast densities, it would seem appropriate to consider a model's density forecasting performance.…”

The Out-of-Sample Success of Term Structure Models as Exchange Rate Predictors: A Step Beyond

“…With regard to the evaluation of forecasting models, although the relevant literature has traditionally focused on accuracy evaluations based on point forecasts, several authors have recently emphasized the importance of evaluating the forecast accuracy of economic models on the basis of density -as opposed to point -forecasting performance (see, inter alia, Diebold, Gunther and Tay, 1998;Granger and Pesaran, 1999;Tay and Wallis, 2000;Timmerman, 2000;Pesaran and Skouras, 2001). Especially when evaluating nonlinear models, which are capable of producing highly non-normal forecast densities, it would seem appropriate to consider a model's density forecasting performance.…”

Efficient Probabilistic Forecasts for Counts

“…The ex ante approach to forecasting that was adopted here differs, of course, from that typically adopted in the forecast literature, in which a forecast distribution is selected (from a set of alternatives) via ex post evaluation based on observed outcomes (see Dawid (1984), Tay and Wallis (2000), Gneiting et al (2007), Gneiting (2008) and Geweke and Amisano (2010) for examples and general discussion, and Czado et al (2009) for an extensive application of such evaluation techniques to discrete count data). However, our approach should not be viewed as a competitor to the fundamental principle of assessing distributional forecasts by using realized outcomes.…”

The Role of Asymmetries and Regime Shifts in the Term Structure of Interest Rates*

“…With regard to the evaluation of forecasting models, although the relevant literature has traditionally focused on accuracy evaluations based on point forecasts, several authors have recently emphasized the importance of evaluating the forecast accuracy of economic models on the basis of density-as opposed to point-forecasting performance (see, e.g., Diebold, Gunther, and Tay 1998;Granger and Pesaran 1999;Tay and Wallis 2000;Timmerman 2000). Especially when evaluating nonlinear models, which are capable of producing highly nonnormal forecast densities, it would seem appropriate to consider a model's density forecasting performance.…”

The Out-of-Sample Success of Term Structure Models as Exchange Rate Predictors: A Step Beyond

“…With regard to the evaluation of forecasting models, although the relevant literature has traditionally focused on accuracy evaluations based on point forecasts, several authors have recently emphasized the importance of evaluating the forecast accuracy of economic models on the basis of density -as opposed to point -forecasting performance (see, inter alia, Diebold, Gunther and Tay, 1998;Granger and Pesaran, 1999;Tay and Wallis, 2000;Timmerman, 2000;Pesaran and Skouras, 2001). Especially when evaluating nonlinear models, which are capable of producing highly non-normal forecast densities, it would seem appropriate to consider a model's density forecasting performance.…”

Efficient Probabilistic Forecasts for Counts

“…The ex ante approach to forecasting that was adopted here differs, of course, from that typically adopted in the forecast literature, in which a forecast distribution is selected (from a set of alternatives) via ex post evaluation based on observed outcomes (see Dawid (1984), Tay and Wallis (2000), Gneiting et al (2007), Gneiting (2008) and Geweke and Amisano (2010) for examples and general discussion, and Czado et al (2009) for an extensive application of such evaluation techniques to discrete count data). However, our approach should not be viewed as a competitor to the fundamental principle of assessing distributional forecasts by using realized outcomes.…”

The Role of Asymmetries and Regime Shifts in the Term Structure of Interest Rates*

“…With regard to the evaluation of forecasting models, although the relevant literature has traditionally focused on accuracy evaluations based on point forecasts, several authors have recently emphasized the importance of evaluating the forecast accuracy of economic models on the basis of density-as opposed to point-forecasting performance (see, e.g., Diebold, Gunther, and Tay 1998;Granger and Pesaran 1999;Tay and Wallis 2000;Timmerman 2000). Especially when evaluating nonlinear models, which are capable of producing highly nonnormal forecast densities, it would seem appropriate to consider a model's density forecasting performance.…”

The Out-of-Sample Success of Term Structure Models as Exchange Rate Predictors: A Step Beyond

“…With regard to the evaluation of forecasting models, although the relevant literature has traditionally focused on accuracy evaluations based on point forecasts, several authors have recently emphasized the importance of evaluating the forecast accuracy of economic models on the basis of density -as opposed to point -forecasting performance (see, inter alia, Diebold, Gunther and Tay, 1998;Granger and Pesaran, 1999;Tay and Wallis, 2000;Timmerman, 2000;Pesaran and Skouras, 2001). Especially when evaluating nonlinear models, which are capable of producing highly non-normal forecast densities, it would seem appropriate to consider a model's density forecasting performance.…”

Efficient Probabilistic Forecasts for Counts

“…The ex ante approach to forecasting that was adopted here differs, of course, from that typically adopted in the forecast literature, in which a forecast distribution is selected (from a set of alternatives) via ex post evaluation based on observed outcomes (see Dawid (1984), Tay and Wallis (2000), Gneiting et al (2007), Gneiting (2008) and Geweke and Amisano (2010) for examples and general discussion, and Czado et al (2009) for an extensive application of such evaluation techniques to discrete count data). However, our approach should not be viewed as a competitor to the fundamental principle of assessing distributional forecasts by using realized outcomes.…”

The Role of Asymmetries and Regime Shifts in the Term Structure of Interest Rates*

“…With regard to the evaluation of forecasting models, although the relevant literature has traditionally focused on accuracy evaluations based on point forecasts, several authors have recently emphasized the importance of evaluating the forecast accuracy of economic models on the basis of density-as opposed to point-forecasting performance (see, e.g., Diebold, Gunther, and Tay 1998;Granger and Pesaran 1999;Tay and Wallis 2000;Timmerman 2000). Especially when evaluating nonlinear models, which are capable of producing highly nonnormal forecast densities, it would seem appropriate to consider a model's density forecasting performance.…”