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Handbook of Economic Forecasting part 84. 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 | 804 T.G. Andersen et al. it follows readily that at h t a2 a 0-5y ft h CTt iit - a2 3-i2 where the long-run or unconditional variance now equals a 1 M 1 - a - 0.5y - ft -1. 3.13 Although the forecasting formula looks almost identical to the one for the GARCH 1 1 model in Equation 3.9 the inclusion of the asymmetric term may materially affect the forecasts by importantly altering the value of the current conditional variance at2 1 t. The news impact curve defined by the functional relationship between 2 -1 and et -1 holding all other variables constant provides a simple way of characterizing the influence of the most recent shock on next periods conditional variance. In the standard GARCH model this curve is obviously quadratic around et-1 0 while the GJR model with y 0 has steeper slopes for negative values of et-1. In contrast the Asymmetric GARCH or AGARCH 1 1 model A t-1 oi a t-1 - y 2 ftat2-1 t-2 3.14 shifts the center of the news impact curve from zero to y affording an alternative way of capturing asymmetric effects. The GJR and AGARCH model may also be combined to achieve even more flexible parametric formulations. Instead of directly parameterizing the conditional variance the EGARCH model is formulated in terms of the logarithm of the conditional variance as in the EGARCH 1 1 model loghA -J rn a zt-1 - E zt-1 YZt-1 ft log a2-1 t-2 3.15 where as previously defined zt t-t1-1 t As for the GARCH model the EGARCH model is readily extended to higher order models by including additional lags on the right-hand side. The parameterization in terms of logarithms has the obvious advantage of avoiding nonnegativity constraints on the parameters as the variance implied by the exponentiated logarithmic variance from the model is guaranteed to be posi-five. As in the GJR and AGARCH models above values of y 0 in the EGARCH model directly captures the asymmetric response or leverage effect. Meanwhile because of the nondifferentiability with respect to zt-1 at zero the .
