March 1, 2008
This paper revisits a number of data-rich prediction methods, like factor models, Bayesian ridge regression and forecast combinations, which are widely used in macroeconomic forecasting, and compares these with a lesser known alternative method: partial least squares regression. Under the latter, linear, orthogonal combinations of a large number of predictor variables are constructed such that these linear combinations maximize the covariance between the target variable and each of the common components constructed from the predictor variables. We provide a theorem that shows that when the data comply with a factor structure, principal components and partial least squares regressions provide asymptotically similar results. We also argue that forecast combinations can be interpreted as a restricted form of partial least squares regression. Monte Carlo experiments confirm our theoretical result that principal components and partial least squares regressions are asymptotically similar when the data has a factor structure. These experiments also indicate that when there is no factor structure in the data, partial least squares regression outperforms both principal components and Bayesian ridge regressions. Finally, we apply partial least squares, principal components and Bayesian ridge regressions on a large panel of monthly U.S. macroeconomic and financial data to forecast, for the United States, CPI inflation, core CPI inflation, industrial production, unemployment and the federal funds rate across different sub-periods. The results indicate that partial least squares regression usually has the best out-of-sample performance relative to the two other data-rich prediction methods.
J.E.L classification codes: C22, C53, E37, E47
Keywords:Macroeconomic forecasting, Factor models, Forecast combination, Principal components, Partial least squares, (Bayesian) ridge regression