Analyzing the Term Structure of Interest Rates Using the Dynamic Nelson-Siegel Model with Time-Varying Parameters

Abstract

In this paper we introduce time-varying parameters in the dynamic Nelson-Siegel yield curve model for the simultaneous analysis and forecasting of interest rates of different maturities, known as the term structure. The Nelson-Siegel model has been recently reformulated as a dynamic factor model where the latent factors are interpreted as the level, slope and curvature of the term structure. The factors are modeled jointly as a vector autoregressive process. We propose to extend this framework in two directions. First, the factor loadings in the Nelson-Siegel yield model depend on a single loading parameter. We allow this parameter to be time-varying by treating it as the fourth latent factor that is modeled jointly with the other factors in the vector autoregressive process. Second, we investigate in detail whether the overall volatility in interest rates is constant over time. For this purpose, we introduce a common volatility component that is specified as a GARCH (generalized autoregressive conditional heteroskedasticity) process. The common volatility component is scaled separately for each maturity by an unknown coefficient. We further investigate whether the innovations of the factors are also subject to a common volatility component. Based on a dataset of yield curves that is analyzed by others, we present empirical evidence of considerable increases in within-sample goodness-of-fit when time-varying loadings and volatilities in the dynamic Nelson-Siegel yield model are introduced.

Keywords: Generalized Autoregressive Conditional Heteroskedasticity model, Extended Kalman filter, Time-Varying Volatility, Yield Curve

JEL Classification: C32, C51, E43