Handbook of Economic Forecasting part 27. 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 | 234 V. Corradi and . Swanson Theorem From Proposition 2 in Corradi and Swanson 2005b . Let CS1 and CS3 hold. Also assume that as T œ I œ and that Tp 0. Then as T P and R œ P rn sup ve e 0 - t roi C v 0. Finally note that in the roiling case F1 P roi V2 P roi can be constructed as in 29 and 30 0 rec and 0t rec with 0 roi and 0t roi and the same statement as in Propositions and hoid. Part III Evaluation of Multiple Misspecified Predictive Models 4. Pointwise comparison of multiple misspecified predictive models In the previous two sections we discussed several in-sample and out of sample tests for the null of either correct dynamic specification of the conditional distribution or for the null of correct conditional distribution for given information set. Needless to say the correct either dynamically or for a given information set conditional distribution is the best predictive density. However it is often sensible to account for the fact that all models may be approximations and so may be misspecified. The literature on point forecast evaluation does indeed acknowledge that the objective of interest is often to choose a model which provides the best loss function specific out-of-sample predictions from amongst a set of potentially misspecified models and not just from amongst models that may only be dynamically misspecified as is the case with some of the tests discussed above. In this section we outline several popular tests for comparing the relative out-of-sample accuracy of misspecified models in the case of point forecasts. We shall distinguish among three main groups of tests i tests for comparing two nonnested models ii tests for comparing two or more nested models and iii tests for comparing multiple models where at least one model is non-nested. In the next section we broaden the scope by considering tests for comparing misspecified predictive density 19 It should be noted that the contents of this section of the chapter have broad
