tailieunhanh - Handbook of Economic Forecasting part 61

Handbook of Economic Forecasting part 61. 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 | 574 G. Elliott Figure 6. Percentiles of difference between OLS and Random Walk forecasts with zt 1 h 4. Percentiles are for 20 10 5 and in ascending order. the difference is roughly h times as large thus is of the same order of magnitude as the variance of the unpredictable component for a h step ahead forecast. The above results present comparisons based on unconditional expected loss as is typical in this literature. Such unconditional results are relevant for describing the outcomes of the typical Monte Carlo results in the literature and may be relevant in describing a best procedure over many datasets however may be less reasonable for those trying to choose a particular forecast model for a particular forecasting situation. For example it is known that regardless of p the confidence interval for the forecast error in the unconditional case is in the case of normal innovations itself exactly normal Magnus and Pesaran 1989 . However this result arises from the normality of yT fi zT and the fact that the forecast error is an even function of the data. Alternatively put the final observation yT zT is normally distributed and this is weighted by values for the forecast model that are symmetrically distributed around zero so for every negative value there is a positive value. Hence overall we obtain a wide normal distribution. Phillips 1979 suggested conditioning on the observed yT presented a method for constructing confidence intervals that condition on this final value of the data for the stationary case. Even in the simplest stationary case these confidence intervals are quite skewed and very different from the unconditional intervals. No results are available for the models considered here. In practice we typically do not know yT zT since we do not know 0. For the best estimates for p we have that T i 2 yT j zT converges to a random variable and hence we cannot even consistently estimate this distance. But the sample is not completely Ch. 11 Forecasting .