Abstract
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.
Highlights
The predictive power of the yield curve for macroeconomic variables has been documented in the literature for a long time
As an alternative to principal components (PC) factors, we propose the use of NS factors in Principal components of predictors X (CI-PC): Let X ∈ RT × N be a matrix of regressors and let
While the combining forecasts (CF)-PC method can be used for data of many kinds, the CF-NS method we propose is tailored to forecasting using the yield curve
Summary
The predictive power of the yield curve for macroeconomic variables has been documented in the literature for a long time. Econometrics 2018, 6, 40 expectations model to investigate the reasons for the success of the slope of the yield curve (the spread between long-term and short-term government bond rates) in predicting real economic activity and inflation. To the PC factor approach on the large-N predictor information set, Diebold and Li (2006) propose the Nelson and Siegel (1987) (NS) factors for the large-N yields They use a modified three-factor NS model to capture the dynamics of the yield curve and show that the three NS factors may be interpreted as level, slope, and curvature. The PC and NS factors of the yield curve are not supervised for a specific variable to forecast These factors combine information (CI) of many predictors (yields) without having to look at a forecast target.
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