tailieunhanh - Handbook of Economic Forecasting part 70

Handbook of Economic Forecasting part 70. 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 | 664 E. Ghysels et al. The final substantive section of this chapter turns to the interactions of seasonality and seasonal adjustment which is important due to the great demand for seasonally adjusted data. This section demonstrates that such adjustment is not separable from forecasting the seasonal series. Further we discuss the feedback from seasonal adjustment to seasonality that exists when the actions of policymakers are considered. In addition to general conclusions Section 6 draws some implications from the chapter that are relevant to the selection of a forecasting model in a seasonal context. 2. Linear models Most empirical models applied when forecasting economic time series are linear in parameters for which the model can be written as ySn s RSn s XSn s 2 p L xSn s USn s 3 where ySn s s 1 . S n 0 . T - 1 represents the observable variable in season . month or quarter s of year n the polynomial L contains any unit roots in ySn s and will be specified in the following subsections according to the model being discussed L represents the conventional lag operator LkxSn s xSn s-k k 0 1 . the driving shocks wSn s of 3 are assumed to follow an ARMA p q 0 p q process such as P L uSn s 0 L eSn s where the roots of 3 z 1 - p 1 Pjzj 0 and 0 z 1 52q 1 0jzj 0 lie outside the unit circle z 1 with eSn s iid 0 a2 . The term s represents a deterministic kernel which will be assumed to be either i a set of seasonal means . Xf 1 8sDs Sn s where Di Sn s is a dummy variable taking value 1 in season i and zero elsewhere or ii a set of seasonals with a nonseasonal time trend . f 1 8sDs Sn s r Sn s . In general the second of these is more plausible for economic time series since it allows the underlying level of the series to trend over time whereas Sn s 8s implies a constant underlying level except for seasonal variation. When considering forecasts we use T to denote the total observed sample size with forecasts required for the future period T h for h 1 2 . Linear