Handbook of Economic Forecasting part 14. 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 | 104 . West standard results from Hansen 1982 can be extended to account for parameter estimation in out of sample tests of instrument residual orthogonality when a fixed parameter estimate is used to construct the test. Christiano 1989 and most of the forecasting literature by contrast updates parameter estimate as forecasts progress through the sample. A general analysis was first presented in West 1996 who showed how standard results can be extended when a sequence of parameter estimates is used and for the mean of a general loss or utility function. Further explication of developments in inference about predictive ability requires me to start writing out some results. I therefore call a halt to the historical summary. The next section begins the discussion of analytical results related to the papers cited here. 3. A small number of nonnested models Part I Analytical results are clearest in the unusual in economics case in which predictions do not rely on estimated regression parameters an assumption maintained in this section but relaxed in future sections. Notation is as follows. The object of interest is Eft an m x 1 vector of moments of predictions or prediction errors. Examples include MSPE mean prediction error mean absolute prediction error covariance between one model s prediction and another model s prediction error mean utility or profit and means of loss functions that weight positive and negative errors asymmetrically as in Elliott and Timmermann 2003 . If one is comparing models then the elements of Eft are expected differences in performance. For MSPE comparisons and using the notation of the previous section for example Eft Ee2t - Ee2t. As stressed by Diebold and Mariano 1995 this framework also accommodates general loss functions or measures of performance. Let Egit be the measure of performance of model i - perhaps MSPE perhaps mean absolute error perhaps expected utility. Then when there are two models m 1 and Eft Eg1t - Eg2t. We have a .
