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Handbook of Economic Forecasting part 85

Handbook of Economic Forecasting part 85. 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 | 814 T.G. Andersen et al. As discussed in Section 3.6 even if the one-step-ahead conditional distribution is known by assumption the corresponding multi-period distributions are not available in closed-form and are generally unknown. Some of the complications that arise in this situation have been discussed in Baillie and Bollerslev 1992 who also consider the use of a Cornish-Fisher expansion for approximating specific quantiles in the multi-step-ahead predictive distributions. Numerical techniques for calculating the predictive distributions based on importance sampling schemes were first implemented by Geweke 1989b . Other important results related to the distribution of temporally aggregated GARCH models include Drost and Nijman 1993 Drost and Werker 1996 and Meddahi and Renault 2004 . 4. Stochastic volatility This section introduces the general class of models labeled Stochastic Volatility SV . In the widest sense of the term SV models simply allow for a stochastic element in the time series evolution of the conditional variance process. For example GARCH models are SV models. The more meaningful categorization which we adopt here is to contrast ARCH type models with genuine SV models. The latter explicitly includes an unobserved nonmeasurable shock to the return variance into the characterization of the volatility dynamics. In this scenario the variance process becomes inherently latent so that - even conditional on all past information and perfect knowledge about the data generating process - we cannot recover the exact value of the current volatility state. The technical implication is that the volatility process is not measurable with respect to observable past information. Hence the assessment of the volatility state at day t changes as contemporaneous or future information from days t j j 0 is incorporated into the analysis. This perspective renders estimation of latent variables from past data alone filtering as well as from all available including future