Handbook of Economic Forecasting part 29. 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 | 254 V. Corradi and . Swanson see . White 1982 Vuong 1989 Giacomini 2002 and Kitamura 2002 . In particular choose model 1 over model 2 if E log fi Yt Zt 0 - log f2 Yt Zt 4 0. For the iid case Vuong 1989 suggests a likelihood ratio test for choosing the conditional density model that is closer to the true conditional density in terms of the KLIC. Giacomini 2002 suggests a weighted version of the Vuong likelihood ratio test for the case of dependent observations while Kitamura 2002 employs a KLIC based approach to select among misspecified conditional models that satisfy given moment Furthermore the KLIC approach has recently been employed for the evaluation of dynamic stochastic general equilibrium models see . Schorfheide 2000 Fernandez-Villaverde and Rubio-Ramirez 2004 and Chang Gomes and Schorfheide 2002 . For example Fernandez-Villaverde and Rubio-Ramirez 2004 show that the KLIC-best model is also the model with the highest posterior probability. The KLIC is a sensible measure of accuracy as it chooses the model which on average gives higher probability to events which have actually occurred. Also it leads to simple likelihood ratio type tests which have a standard limiting distribution and are not affected by problems associated with accounting for PEE. However it should be noted that if one is interested in measuring accuracy over a specific region or in measuring accuracy for a given conditional confidence interval say this cannot be done in as straightforward manner using the KLIC. For example if we want to evaluate the accuracy of different models for approximating the probability that the rate of inflation tomorrow given the rate of inflation today will be between and say we can do so quite easily using the square error criterion but not using the KLIC. . A predictive density accuracy test for comparing multiple misspecified models Corradi and Swanson 2005a 2006b introduce a measure of distributional accuracy which can be .
