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Handbook of Economic Forecasting part 16

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Handbook of Economic Forecasting part 16. 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 | 124 K.D. West Observe that X 1 for the recursive scheme this is an example in which there is the cancellation of variance and covariance terms noted in point 3 at the end of Section 4. For the fixed scheme X 1 with X increasing in P R. So uncertainty about parameter estimates inflates the variance with the inflation factor increasing in the ratio of the size of the prediction to regression sample. Finally for the rolling scheme X 1. So use of 6.8 will result in smaller standard errors and larger t-statistics than would use of a statistic that ignores the effect of uncertainty about p . The magnitude of the adjustment to standard errors and t-statistics is increasing in the ratio of the size of the prediction to regression sample. 5. If p 0 and if the rolling or fixed but not the recursive scheme is used apply the encompassing test just discussed setting f P-1 XT R e1t 1X t 1fi2t Note that in contrast to the discussion just completed there is no over e1t 1 because model 1 is nested in model 2 p 0 means p 0 so e1t 1 yt 1 and e1t 1 is observable. One can use standard results - asymptotic irrelevance applies. The factor of X that appears in 7.2 resulted from estimation of p and is now absent. So V V if for example e1t is i.i.d. one can consistently estimate V with V P-1 T R e1t 1X 2t 1P2P 2 9 6. If the rolling or fixed regression scheme is used construct a conditional rather than unconditional test Giacomini and White 2003 . This paper makes both methodological and substantive contributions. The methodological contributions are twofold. First the paper explicitly allows data heterogeneity e.g. slow drift in moments . This seems to be a characteristic of much economic data. Second while the paper s conditions are broadly similar to those of the work cited above its asymptotic approximation holds R fixed while letting P x . The substantive contribution is also twofold. First the objects of interest are moments of e1t and e2t rather than et. Even in nested models e1t and