This chapter reviews different methods to construct density forecasts and to aggregate forecasts from many sources. Density evaluation tools to measure the accuracy of density forecasts are reviewed and calibration methods for improving the accuracy of forecasts are presented. The manuscript...

A Bayesian semi-parametric dynamic model combination is proposed in order to deal with a large set of predictive densities. It extends the mixture of experts and the smoothly mixing regression models by allowing combination weight dependence between models as well as over time. It introduces an...

In this paper we expand the literature of risk neutral density estimation across maturities from implied volatility curves, usually estimated and interpolated through cubic smoothing splines. The risk neutral densities are computed through the second derivative as in Panigirtzoglou and...

A flexible forecast density combination approach is introduced that can deal with large data sets. It extends the mixture of experts approach by allowing for model set incompleteness and dynamic learning of combination weights. A dimension reduction step is introduced using a sequential...

A Bayesian dynamic compositional model is introduced that can deal with combining a large set of predictive densities. It extends the mixture of experts and the smoothly mixing regression models by allowing for combination weight dependence across models and time. A compositional model with...

Using a Bayesian framework this paper provides a multivariate combination approach to prediction based on a distributional state space representation of predictive densities from alternative models. In the proposed approach the model set can be incomplete. Several multivariate time-varying...

We propose a Bayesian combination approach for multivariate predictive densities which relies upon a distributional state space representation of the combination weights. Several specifications of multivariate time-varying weights are introduced with a particular focus on weight dynamics driven...

Using a Bayesian framework this paper provides a multivariate combination approach to prediction based on a distributional state space representation of predictive densities from alternative models. In the proposed approach the model set can be incomplete. Several multivariate time-varying...

We propose a multivariate combination approach to prediction based on a distributional state space representation of the weights belonging to a set of Bayesian predictive densities which have been obtained from alternative models. Several specifications of multivariate time-varying weights are...