TAILIEUCHUNG - Handbook of Economic Forecasting part 86

Handbook of Economic Forecasting part 86. 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 | 824 . Andersen et al. sample. Without going into specifics an appropriate procedure may be developed to obtain a close approximation to this conditional density within a class of SNP densities which are analytically tractable and allow for explicit computation of the associated score vector. The leading term will typically consist of a GARCH type model. Essentially the information regarding the probabilistic structure available from the data is being encoded into an empirically tractable SNP representation so that for a large enough sample we have g rt xt-i fir f rt St-1 0q where g rt xt -1 fr denotes the fitted SNP density evaluated at the pseudo maximum likelihood estimate fr and 00 denotes the true unknown parameter vector of the model generating the data under the null hypothesis. In general the functional form of g is entirely different from the unknown f and hence there is no direct compatibility between the two parameter vectors f and 0 although we require that the dimension of f is at least as large as that of 0. Notice how this SNP representation sidesteps the lack of a tractable expression for the likelihood contribution as given by the middle term in the likelihood expression in . Although the SNP density is not used for formal likelihood estimation it is used to approximate the efficient score moments. By construction fr satisfies a set of first order conditions for the pseudo loglikelihood function under the empirical measure induced by the data that is letting r t rt xt-1 it holds that 1 9 1 V V logg rt xt-i fr y2 r Lt q- T 7 df I It is clear that takes the form of pseudo score moments. This representation of the data through a set of efficient moment conditions is the key part of the projection step of EMM. The data structure has effectively been projected onto an analytically tractable class of SNP densities augmented as appropriate by a leading dynamic GARCH term. Since we are working under the assumption that we have a good

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