Handbook of Economic Forecasting part 71. 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 | 674 E. Ghysels et al. each of the seasonal frequencies. However even if this autocorrelation is not accounted for S in 26 canbe consistently estimated. Although we would again expect a forecaster to recognize the presence of autocorrelation the noninvertible moving average process cannot be approximated through the usual practice of autoregressive augmentation. Hence as an extreme case we again examine the consequences of a naive researcher assuming us s to be iid. Now using the representation considered in 13 to derive the level forecast from a seasonally integrated model it follows that E yr 1 - yr i r 2 E JL .I2 yr lyD r i er i I - yr i-s Asyr i r with yr i-s yr-s 52 s i S Di r i-s er i-s. Note that although the seasonally integrated model apparently makes no allowance for the deterministic seasonality in the DGP this deterministic seasonality is also present in the past observation yr i-s on which the forecast is based. Hence since Di r i Di r i-s the deterministic seasonality cancels between yr and yr -s so that E yr i - yr i r 2 E yr er i - yr-s er i-s 2 E yr - yr-s - S er i - er i-s 2 E er er-i er-s i er i - er i-s 2 E er i er ------ er-s 2 2 sa2 as from 26 the naive forecaster uses Asyr i S. The result also uses 26 to substitute for yr - yr-s. Thus as a consequence of seasonal overdifferencing the MSFE increases proportionally to the periodicity of the data. This MSFE effect can however be reduced if the overdifferencing is partially accounted for through augmentation. Now consider the use of the SARIMA model when the data is in fact generated by 25 . Although AiAsys s Ases s 27 we again consider the naive forecaster who assumes vsn s Ases s is iid. Using 7 and noting from 27 that the forecaster uses Ai Asyr i 0 it follows that E yr i - yr i r 2 E s 2 yr 2 S Di r i er i - yr i-s Asyr I E er i - er i-s 2 2a2. Once again the deterministic seasonal pattern is taken into account indirectly through the implicit dependence of the forecast on the past observed .
