Forecasting with Factor-Augmented Regression: A Frequentist Model Averaging Approach, Second Version
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 across models 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 asymptotically unbiased estimators of the one-step-ahead and multi-step-ahead mean squared forecast errors, respectively, provided that N, T → ∞. (However, the paper does not establish any optimality properties for the methods.) In contrast to well-known results in the literature, this result suggests that 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.