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The growing availability of financial and macroeconomic data sets including a large number of time series (hence the high dimensionality) calls for econometric methods providing a convenient and parsimonious representation of the covariance structure both in the time and the cross-sectional dimensions. Currently, dynamic factor models constitute the dominant framework across many disciplines for formal compression of information. Recent econometric research has produced a rich body of theory for the estimation of these models and their subsequent use for forecasting and for the estimation of structural economic models. To overcome the challenges of dimensionality, many forecast approaches proceed by somehow reducing the number of predictors. Principal component regression (PCR) approach proposes computing forecasts as projection on the first few principal components of the predictors. Bayesian model averaging (BMA) approach combines forecasts to extract information from different possible relationships between the predicted variable and the predictor variables. These two literature apparently moved in two different directions. However, recent findings by De Mol et al. [2008] and the Ouysse and Kohn [2009] suggest there are theoretical and practical reasons to connect the two literatures. This paper provides empirical evidence for connecting these two seemingly different approaches to forecasting. We study the performance of BMA as a forecasting method based on large panels of time series as an alternative to PCR. We show empirically that these forecasts are highly correlated implying similar mean-square forecast errors. Applied to forecasting Industrial production and inflation in the United States, we find that the set of variables deemed informative changes over time which suggest temporal instability. The results can also be driven by the nature of the macroeconomic data which is characterized by collinearity and that the variable selection is sensitive to minor perturbations of the data. The empirical results serve as a preliminary guide to understanding the behavior of BMA under double asymptotics, i.e. when the cross-section and the sample size become large.

Comparison of Bayesian Moving Average and Principal Component Forecasts for large dimensional factor models