On multicollinearity and the value of the shape parameter in the term structure Nelson-Siegel model

This paper investigates the sensitivity of the dynamic Nelson-Siegel factor loadings to the value of the shape parameter, lambda. It also analyses the multicollinearity problem and addresses how to mitigate this issue in the estimation process. First, we find that the selection of a fixed lambda is not optimal due to the collinearity problems. Second, we observe a substantial difference between the forecasting performance of the traditional estimation procedures and that of the ridge regression approach. Finally, we implement a Monte Carlo simulation exercise in order to study the statistical distribution of the estimates of the model parameters and thus determine the extent to which they differ from the real values. Furthermore, we find that multicollinearity between the factors of the NS model can, in the case of ordinary least squares estimation with a fixed parameter lambda result in greater differences between the estimates and the actual parameter values. Ridge regression corrects such differences and produces more stable estimates than the ordinary linear and nonlinear least squares methods.