### Download Handbook of Economic Forecasting (Handbooks in Economics) by G. Elliott, C. W.J. Granger, A. G. Timmermann PDF

• March 28, 2017
• Economy
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By G. Elliott, C. W.J. Granger, A. G. Timmermann

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In fact latent variables are, formally, no different from hyperparameters. For the stochastic volatility model Equations (4)–(5) provide the distribution of the latent variables (hyperparameters) conditional on the parameters, just as (12) provides the hyperparameter distribution in the illustration of shrinkage. Conditional on the latent variables {ht }, (6) indicates the observables distribution, just as (14) indicates the distribution of observables conditional on the parameters. In the formal generalization of this idea the complete model provides a conventional prior distribution p(θ A | A), and then the distribution of a vector of latent variables z 14 J.

YT +F ). The predictive density of yT +1 , . . , yT +F , conditional on the data YoT and a particular model A is p yT +1 , . . , yT +F | YoT , A . (21) The predictive density is relevant after formulation of the model A and observing YT = YoT , but before observing yT +1 , . . , yT +F . Once yT +1 , . . , yT +F are known, we can evaluate (21) at the observed values. This yields the predictive likelihood of yoT +1 , . . , yoT +F conditional on YoT and the model A, the real number p(yoT +1 , .

It dates at least to the 1963 work of Barnard (1963) in a paper that studied airline data. This was followed by a series of influential papers by Granger and coauthors [Bates and Granger (1969), Granger and Ramanathan (1984), Granger (1989)]; Clemen (1989) provides a review of work before 1990. The papers in this and the subsequent forecast combination literature all addressed the question of how to produce a superior forecast given competing alternatives. The answer turns in large part on what is available.