Forecasting with many predictors is of interest, for instance, in macroeconomics and finance. The forecast accuracy of two methods for dealing with many predictors is compared, that is, principal component regression (PCR) and principal covariate regression (PCovR). Simulation experiments with data generated by factor models and regression models indicate that, in general, PCR performs better for the first type of data and PCovR performs better for the second type of data. An empirical application to four key US macroeconomic variables shows that PCovR achieves improved forecast accuracy in some situations.

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Keywords Factor model, Macroeconomic forecasting, Principal components, Principal covariates, Regression model
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Heij, C., van Dijk, D.J.C., & Groenen, P.J.F.. (2007). Forecast comparison of principal component regression and principal covariate regression. Computational Statistics & Data Analysis, 51(7), 3612–3625. doi:10.1016/j.csda.2006.10.019