tailieunhanh - Handbook of Economic Forecasting part 82

Handbook of Economic Forecasting part 82. 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 | 784 T. G. Andersen et al. the Brownian motion process the return variation should be related to the cumulative integrated spot variance. It is indeed possible to formalize this intuition the conditional return variation is linked closely and - under certain conditions in an ex-post sense - equal to the so-called integrated variance volatility IV t j a2 s ds. We provide more in-depth discussion and justification for this integrated volatility measure and its relationship to the conditional return distribution in Section 4. It is however straightforward to motivate the association through the approximate discrete return process r t A introduced above. If the variation in the drift is an order of magnitude less than the variation in the volatility over the t - 1 t time interval - which holds empirically over daily or weekly horizons and is consistent with a no-arbitrage condition - it follows for small infinitesimal time intervals A Var r t F_ E 1 A a 2 i Ly 1 - J A A J F _i E lV t I F _i . Hence the integrated variance measure corresponds closely to the conditional variance o -p for discretely sampled returns. It represents the realized volatility over the same one-period-ahead forecast horizon and it simply reflects the cumulative impact of the spot volatility process over the return horizon. In other words integrated variances are ex-post realizations that are directly comparable to ex-ante volatility forecasts. Moreover in contrast to the one-period-ahead squared return innovations which as discussed in the context of are plagued by large idiosyncratic errors the integrated volatility measure is not distorted by error. As such it serves as an ideal theoretical ex-post benchmark for assessing the quality of ex-ante volatility forecasts. To more clearly illustrate these differences between the various volatility concepts Figure 1 graphs the simulations from a continuous-time stochastic volatility process. The simulated model is designed to induce temporal .