Estimating the spot rate curve using the Nelson–Siegel model

The Nelson–Siegel model is widely used in practice for fitting the term structure of interest rates. Due to the ease in linearizing the model, a grid search or an OLS approach using a fixed shape parameter are popular estimation procedures. The estimated grid search parameters, however, have been reported (1) to behave erratically over time, and (2) to have relatively large variances. On the other hand, parameter estimates based on a fixed shape parameter, while avoiding multicollinearity, turn out to be too smooth. We show that the Nelson–Siegel model can become heavily collinear depending on the estimated/fixed shape parameter. A simple procedure based on ridge regression can remedy the reported problems significantly.