tailieunhanh - Handbook of Economic Forecasting part 63

Handbook of Economic Forecasting part 63. 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 | 594 G. Elliott where M is as before and is asymptotically independent of the standard Brownian motion . Now the usefulness of the decomposition of the parameter estimator into two parts can be seen through examining what each of these terms look like asymptotically when suitably scaled. The first term by virtue of nit being orthogonal to the entire history of xt will when suitably scaled have an asymptotic mixed normal distribution. The second term is exactly what we would obtain apart from being multiplied at the front by f in the Dickey and Fuller 1979 regression of xt on a constant and lagged dependent variable. Hence this term has the familiar nonstandard distribution from that regression when standardized in the same way as the first term. Also by virtue of the independence of n1t and e2t each of these terms is asymptotically independent. Thus the limit distribution for the standardized coefficients is a weighted sum of a mixed normal and a Dickey and Fuller 1979 distribution which will not be well approximated by a normal distribution. Now consider the t statistic testing p 0. The t statistic testing the hypothesis that p1 0 when this is the null is typically employed to justify the regressors inclusion in the forecasting equation. This t statistic has an asymptotic distribution given by tpi 0 1 - 52 1 2z 3DF where z is distributed as a standard normal and DF is the usual Dickey and Fuller t distribution when c 1 1 and y 0 and a variant of it otherwise. The actual distribution is DF Md 1 2 - Md 0 2 - c 1 2 f Md s ds where Md s is the projection of M s on the continuous analog of zt. When y 0 c 1 1 and at least a constant term is included this is identical to the usual DF distribution with the appropriate order of deterministic terms. When c 1 is not one we have an extra effect through the serial correlation cf. Phillips 1987 . The nuisance parameter that determines the weights 3 is the correlation between the shocks driving the forecasting equation .