Comparing term structure estimation techniques : an exercise with Brazilian data

This text evaluates the empirical models of the Term Structure of Interest Rates (TSIR), comparing the resulting estimates regarding goodness-of-fit, robustness to outliers, and smoothness. In addition to the descriptive statistics on these metrics, the Friedman test and the multiple comparison procedure were used to assess the statistical significance of differences among the models. Literature usually considers nonparametric or spline models in addition to the parsimonious function models derived from Nelson and Siegel (1987). We expand this set of models by considering local regression (Loess) and two Kernel regression specifications. We used data from Brazilian interest rate derivatives over 1,313 working days. The Smoothing Spline consistently has the best-fit in-sample but is outperformed by the Loess out-of-sample on all different maturity ranges. Furthermore, the Smoothing Spline and the Loess are robust and have the best fit even in the presence of outliers. Among the Nelson-Siegel family models, the more parametrised versions have no clear advantage regarding goodness-of-fit. Considering the surveyed literature, applying Loess and Kernel regression and the use of multiple comparison procedure in the context of yield curve estimation are novel contributions.