Handbook of Economic Forecasting part 19. 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 | 154 A. Timmermann that both have access to the same information set and use the same model to forecast the mean and variance of Y lyt h t A h 1. Their forecasts are then computed as assuming normality cf. Christoffersen and Diebold 1997 yt h t 1 dyt h t oyt h t yt h t 2 dyt h t oyt h r Each forecast includes an optimal bias whose magnitude is time-varying. For a forecast user with symmetric loss neither of these forecasts is particularly useful as each is biased. Furthermore the bias cannot simply be taken out by including a constant in the forecast combination regression since the bias is time-varying. However in this simple case there exists an exact linear combination of the two forecasts that is unbiased yf i t oyyt h t 1 1 - M yt h t 2 m - . ai -2 Of course this is a special case but it nevertheless does show how biases in individual forecasts can either be eliminated or reduced in a forecast combination. . Combining as a hedge against non-stationarities Hendry and Clements 2002 argue that forecast combinations may work well empirically because they provide insurance against what they refer to as extraneous deterministic structural breaks. They consider a wide array of simulation designs for the break and find that combinations work well under a shift in the intercept of a single variable in the data generating process. In addition when two or more positively correlated predictor variables are subject to shifts in opposite directions forecast combinations can be expected to lead to even larger reductions in the MSE. Their analysis considers the case where a break occurs after the estimation period and does not affect the parameter estimates of the individual forecasting models. They establish conditions on the size of the post-sample break ensuring that an equal-weighted combination out-performs the individual In support of the interpretation that structural breaks or model instability may explain the good average performance of forecast .
