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; T! 1: 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 …nd that they compare favorably to many popular shrinkage-type forecasting methods. JEL Classi…cation: C52, C53 Keywords: Cross-validation, factor models, forecast combination, generated regressors, Mallows

1 Mild factor loading instability, particularly if sufficiently independent across the different constituent variables, does not affect the estimation of the number of factors, nor sub-sequent estimation of the factors themselves (see e.g. Stock and Watson (2009)). This result does not hold in the presence of large common breaks in the factor loadings, how-ever. In this case, information criteria overestimate the number of breaks. Additionally, estimated factors are no longer consistent estimators of “true ” factors. Hence, various recent research papers in the diffusion index literature focus on testing the constancy of factor loadings. One reason why this is a positive development is that in applied work, factor augmented forecasting models are used widely for prediction, and it is important to understand when such models are stable. Now, forecast failure of factor augmented

This chapter reviews methods for selecting empirically relevant predictors from a set of N potentially relevant ones for the purpose of forecasting a scalar time series. I first discuss criterion based procedures in the conventional case when N is small relative to the sample size, T. I then turn to the large N case. Regularization and dimension reduction methods are then discussed. Irrespective of the model size, there is an unavoidable tension between prediction accuracy and consistent model determination. Simulations are used to compare selected methods from the perspective of relative risk in one period ahead forecasts.

This dissertation consists of two essays on testing hypotheses in panel data models when non-stationarity exists in the model. This is done under the high-dimensional framework where both n (cross-section dimension) and T (time series dimension) are large. In the first essay, I discuss the limiting distribution of the t-statistic for H0: = 0 using different panel data estimators and propose using the t-statistic based on Feasible GLS estimator. In the second essay, I develop the bootstrap F-statistic for cross-sectional independence in a panel data model with factor structure. The first essay considers the problem of hypotheses testing in a simple panel data regression model with random individual effects and serially correlated dis-turbances. Following Baltagi, Kao and Liu (2008), I allow for the possibility of non-stationarity in the regressor and/or the disturbance term. While Baltagi et al. (2008) focus on the asymptotic properties and distributions of the standard panel data estimators, this essay focuses on test of hypotheses in this setting. One impor-

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inference for linear dynamic panel data models with

UNU-MERIT Working Papers intend to disseminate preliminary results of research carried out at UNU-MERIT and MGSoG to stimulate discussion on the issues raised. How important is innovation? A Bayesian factor-augmented productivity model on panel data.