Forecasting with Many Predictors
Historically, time series forecasts of economic variables have used only a handful of predictor variables, while forecasts based on a large number of predictors have been the province of judgmental forecasts and large structural econometric models. The past decade, however, has seen considerable progress in the development of time series forecasting methods that exploit many predictors, and this chapter surveys these methods. The first group of methods considered is forecast combination (forecast pooling), in which a single forecast is produced from a panel of many forecasts. The second group of methods is based on dynamic factor models, in which the comovements among a large number of economic variables are treated as arising from a small number of unobserved sources, or factors. In a dynamic factor model, estimates of the factors (which become increasingly precise as the number of series increases) can be used to forecast individual economic variables. The third group of methods is Bayesian model averaging, in which the forecasts from very many models, which differ in their constituent variables, are averaged based on the posterior probability assigned to each model. The chapter also discusses empirical Bayes methods, in which the hyperparameters of the priors are estimated. An empirical illustration applies these different methods to the problem of forecasting the growth rate of the U.S. index of industrial production with 130 predictor variables.
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