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

Tinbergen Institute Discussion Paper No. 07-095/4

Journal of Business and Economic Statistics, Vol. 28, No. 3, pp. 329-343, 2010

31 Pages Posted: 10 Dec 2007 Last revised: 15 Aug 2011

See all articles by Siem Jan Koopman

Siem Jan Koopman

Vrije Universiteit Amsterdam - School of Business and Economics; Tinbergen Institute; Aarhus University - CREATES

Max Mallee

Vrije Universiteit Amsterdam, School of Business and Economics

Michel van der Wel

Erasmus University Rotterdam

Date Written: June 11, 2008

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

Suggested Citation

Koopman, Siem Jan and Mallee, Max and van der Wel, Michel, Analyzing the Term Structure of Interest Rates Using the Dynamic Nelson-Siegel Model with Time-Varying Parameters (June 11, 2008). Tinbergen Institute Discussion Paper No. 07-095/4, Journal of Business and Economic Statistics, Vol. 28, No. 3, pp. 329-343, 2010, Available at SSRN: https://ssrn.com/abstract=1068861 or http://dx.doi.org/10.2139/ssrn.1068861

Siem Jan Koopman (Contact Author)

Vrije Universiteit Amsterdam - School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081 HV
Netherlands
+31205986019 (Phone)

HOME PAGE: http://sjkoopman.net

Tinbergen Institute ( email )

Gustav Mahlerplein 117
1082 MS Amsterdam
Netherlands

HOME PAGE: http://personal.vu.nl/s.j.koopman

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Max Mallee

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

Michel Van der Wel

Erasmus University Rotterdam ( email )

Burg. Oudlaan 50
Rotterdam, NL 3062 PA
Netherlands

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
1,211
Abstract Views
4,793
Rank
34,630
PlumX Metrics