Using the Entire Yield Curve in Forecasting Output and Inflation

In forecasting a variable (forecast target) using many predictors, a factor model with principal components (PC) is often used. When the predictors are the yield curve (a set of many yields), the Nelson–Siegel (NS) factor model is used in place of the PC factors. These PC or NS factors are combining information (CI) in the predictors (yields). However, these CI factors are not “supervised” for a specific forecast target in that they are constructed by using only the predictors but not using a particular forecast target. In order to “supervise” factors for a forecast target, we follow Chan et al. (1999) and Stock and Watson (2004) to compute PC or NS factors of many forecasts (not of the predictors), with each of the many forecasts being computed using one predictor at a time. These PC or NS factors of forecasts are combining forecasts (CF). The CF factors are supervised for a specific forecast target. We demonstrate the advantage of the supervised CF factor models over the unsupervised CI factor models via simple numerical examples and Monte Carlo simulation. In out-of-sample forecasting of monthly US output growth and inflation, it is found that the CF factor models outperform the CI factor models especially at longer forecast horizons.