Staff Report, Federal Reserve Bank of New York 327
We compare a number of data-rich prediction methods that are widely used in macroeconomic forecasting with a lesser known alternative: partial least squares (PLS) regression. In this method, linear, orthogonal combinations of a large number of predictor variables are constructed such that the covariance between a target variable and these common components is maximized. We show theoretically that when the data have a factor structure, PLS regression can be seen as an alternative way to approximate this unobserved factor structure. In addition, we prove that when a large data set has a weak factor structure, which possibly vanishes in the limit, PLS regression still provides asymptotically the best fit for the target variable of interest. Monte Carlo experiments confirm our theoretical results that PLS regression performs at least as well as principal components regression and rivals Bayesian regression when the data have a factor structure. But when the factor structure in the data is weak, PLS regression outperforms both principal components and Bayesian regressions. Finally, we apply PLS, principal components, and Bayesian regressions to a large panel of monthly U.S. macroeconomic data to forecast key variables across different subperiods. The results indicate that PLS regression usually has the best out-of-sample performance.
Macroeconomic forecasting factor models forecast combination principal components partial least squares Bayesian ridge regression