Handbook of Economic Forecasting part 5. Research on forecasting methods has made important progress over recent years and these developments are brought together in the Handbook of Economic Forecasting. The handbook covers developments in how forecasts are constructed based on multivariate time-series models, dynamic factor models, nonlinear models and combination methods. The handbook also includes chapters on forecast evaluation, including evaluation of point forecasts and probability forecasts and contains chapters on survey forecasts and volatility forecasts. Areas of applications of forecasts covered in the handbook include economics, finance and marketing | 14 J. Geweke and C. Whiteman conditional on 0A p z 0 A A . The observables distribution typically involves both z and 0A p YT z 0A A . Clearly one could also have a hierarchical prior distribution for 0 A in this context as well. Latent variables are convenient but not essential devices for describing the distribution of observables just as hyperparameters are convenient but not essential in constructing prior distributions. The convenience stems from the fact that the likelihood function is otherwise awkward to express as the reader can readily verify for the stochastic volatility model. In these situations Bayesian inference then has to confront the problem that it is impractical if not impossible to evaluate the likelihood function or even to provide an adequate numerical approximation. Tanner and Wong 1987 provided a systematic method for avoiding analytical integration in evaluating the likelihood function through a simulation method they described as data augmentation. Section provides an example. This ability to use latent variables in a routine and practical way in conjunction with Bayesian inference has spawned a generation of Bayesian time series models useful in prediction. These include state space mixture models see Carter and Kohn 1994 1996 and Gerlach Carter and Kohn 2000 discrete state models see Albert and Chib 1993 and Chib 1996 component models see West 1995 and Huerta and West 1999 and factor models see Geweke and Zhou 1996 and Aguilar and West 2000 . The last paper provides a full application to the applied forecasting problem of foreign exchange portfolio allocation. . Model combination and evaluation In applied forecasting and decision problems one typically has under consideration not a single model A but several alternative models A1 . AJ. Each model is comprised of a conditional observables density 1 a conditional density of a vector of interest 8 and a prior density 9 . For a finite number of models each fully articulated in this
