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Handbook of Economic Forecasting part 67. 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 | 634 M.P. Clements and D.F. Hendry which is more than double the conditional expectation forecast error variance V vT h xT . Clearly there is a bias-variance trade-off bias can be reduced at the cost of an inflated forecast-error variance. Notice also that the second term in 57 is of the order of h2 so that this trade-off should be more favorable to intercept correcting at short horizons. Furthermore basing ICs on averages of recent errors rather than the period T error alone may provide more accurate estimates of the break and reduce the inflation of the forecast-error variance. For a sufficiently large change in t o the adjusted forecasts will be more accurate than those of unadjusted forecasts on squared-error loss measures. Detailed analyses of ICs can be found in Clements and Hendry 1996 1998 Chapter8 1999 Chapter 6 . 7.3. Differencing Section 4.3 considered the forecast performance of a DVAR relative to a VECM when there were location shifts in the underlying process. Those two models are related by the DVAR omitting the disequilibrium feedback of the VECM rather than by a differencing operator transforming the model used to forecast see e.g. Davidson et al. 1978 . For shifts in the equilibrium mean at the end of the estimation sample the DVAR could outperform the VECM. Nevertheless both models were susceptible to shifts in the growth rate. Thus a natural development is to consider differencing once more to obtain a DDVAR and a DVECM neither of which includes any deterministic terms when linear deterministic trends are the highest needed to characterize data. The detailed algebra is presented in Hendry 2oo5 who shows that the simplest double-differenced forecasting device namely A2xt 1 t 0 58 can outperform in a range of circumstances especially if the VECM omits important explanatory variables and experiences location shifts. Indeed the forecast-error variance of 58 need not be doubled by differencing and could even be less than that of the VECM so 58 would .
