Robust Forecasting by Regularization

Abstract

The prediction of multivariate outcomes in a linear regression setting with a large number of potential regressors is a common problem in macroeconomic and financial forecasting. We exploit that the frequently encountered problem of nearly collinear regressors can be addressed using standard shrinkage type estimation. Moreover, independently of near collinearity issues, when the outcomes are high-dimensional correlated random variables, univariate forecasting is often sub-optimal and can be improved upon by shrinkage based on a canonical correlation analysis. In this paper, we consider a family of models for multivariate prediction that employ both types of shrinkage to identify a parsimonious set of common forecasting factors. The approach is designed to jointly forecast a vector of variables of interest based on a near collinear set of predictors. We illustrate its promising performance in applications to several standard forecasting problems in macroeconomics and finance relative to existing approaches. In particular, we show that a single factor model can almost double the predictability of one-month bond excess returns across a wide maturity range by using a set of predictors combining yield slopes and the maturity related cycles of Cieslak and Povala (2011). Keywords: Out-of-sample forecasting, regularization, reduced rank regression, ridge regression