Inestability presented in the estimating of the Nelson-Siegel-Svensson model

TL;DR

This paper investigates collinearity issues in the Nelson-Siegel-Svensson model, highlighting the instability in parameter estimation and proposing a new ridge regression method to improve estimation stability, demonstrated through empirical data analysis.

Contribution

The paper introduces a novel raise regression method to mitigate collinearity in Nelson-Siegel-Svensson model estimation, addressing limitations of traditional techniques.

Findings

Collinearity causes instability in model coefficient estimates.

Traditional methods like non-linear optimization and ridge regression have drawbacks.

The proposed raise regression improves estimation stability in empirical tests.

Abstract

The literature shows the possible existence of a problem called collinearity in both Nelson-Siegel and Nelson-Siegel-Svensson models due to the relationship between the slope and curvature components. The presence of this problem and the estimation of both models by Ordinary Least Squares would lead to coefficients estimates that may be unstable among other consequences. However, these estimates are used to make monetary policy decisions. For this reason, it is important to try mitigating this collinearity problem. Consequently, some authors propose traditional procedures for the treatment of collinearity such as: non-linear optimisation, to fix the shape parameter or ridge regression. Nevertheless, all these processes have their disadvantages. Alternatively, a new method with good properties called raise regression is proposed in this paper. Finally, the methodologies are illustrated with an empirical comparison on Euribor Overnight Index Swap and Euribor Interest Rates Swap data between 2011 and 2021.