Xu Cheng and Bruce E. Hansen
Forecasting with Factor-Augmented Regression: A Frequentist Model Averaging Approach
Journal of Econometrics, (2015), 186, 280-293.
This paper considers forecast combination with factor-augmented regression. In this framework, a large number of forecasting models are available, varying by the choice of factors and the number of lags. We investigate forecast combination using weights that minimize the Mallows and the leave-h-out cross validation criteria. The unobserved factor regressors are estimated by principle components of a large panel with N predictors over T periods. With these generated regressors, we show that the Mallows and leave-h-out cross validation criteria are approximately unbiased estimators of the one-step-ahead and multi-step-ahead mean squared forecast errors, respectively, provided that N and T diverge to infinity. In contrast to well-known results in the literature, the generated-regressor issue can be ignored for forecast combination, without restrictions on the relation between N and T.
Simulations show that the Mallows model averaging and leave-h-out cross-validation averaging methods yield lower mean squared forecast errors than alternative model selection and averaging methods such as AIC, BIC, cross validation, and Bayesian model averaging. We apply the proposed methods to the U.S. macroeconomic data set in Stock and Watson (2012) and find that they compare favorably to many popular shrinkage-type forecasting methods.
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Some of the above material is based upon work supported by the National Science Foundation under Grants No. SES-9022176, SES-9120576, SBR-9412339, and SBR-9807111.
Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author(s), and do not necessarily reflect the views of the NSF.