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

S.J. Koopman, M.I.P. Mallee, M. van der Wel

Research output: Working paperProfessional

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 modelled by a vector autoregressive process. We propose to extend this framework in two directions. First, the factor loadings are made time-varying through a simple single step function and we show that the model fit increases significantly as a result. The step function can be replaced by a spline function to allow for more smoothness and flexibility. Second, we investigate empirically whether the volatility in interest rates across different time periods is constant. For this purpose, we introduce a common volatility component that is specified as a spline function of time and scaled appropriately for each series. Based on a data-set that is analysed by others, we present empirical evidence where time-varying loadings and volatilities in the dynamic Nelson-Siegel framework lead to significant increases in model fit. Improvements in the forecasting of the term structure are also reported. Finally, we provide an illustration where the model is applied to an unbalanced dataset. It shows that missing data entries can be estimated accurately.
Original languageEnglish
Place of PublicationAmsterdam
PublisherTinbergen Instituut
Publication statusPublished - 2007

Publication series

NameDiscussion paper TI
No.07-095/4

Fingerprint

Term structure of interest rates
Nelson-Siegel model
Time-varying parameters
Term structure
Time-varying
Splines
Interest rates
Missing data
Empirical evidence
Curvature
Yield curve
Latent factors
Maturity
Dynamic factor model
Factors
Volatility components
Factor loadings
Vector autoregressive process

Cite this

Koopman, S. J., Mallee, M. I. P., & van der Wel, M. (2007). Analyzing the Term Structure of Interest Rates using the Dynamic Nelson-Siegel Model with Time-Varying Parameters. (Discussion paper TI; No. 07-095/4). Amsterdam: Tinbergen Instituut.
Koopman, S.J. ; Mallee, M.I.P. ; van der Wel, M. / Analyzing the Term Structure of Interest Rates using the Dynamic Nelson-Siegel Model with Time-Varying Parameters. Amsterdam : Tinbergen Instituut, 2007. (Discussion paper TI; 07-095/4).
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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 modelled by a vector autoregressive process. We propose to extend this framework in two directions. First, the factor loadings are made time-varying through a simple single step function and we show that the model fit increases significantly as a result. The step function can be replaced by a spline function to allow for more smoothness and flexibility. Second, we investigate empirically whether the volatility in interest rates across different time periods is constant. For this purpose, we introduce a common volatility component that is specified as a spline function of time and scaled appropriately for each series. Based on a data-set that is analysed by others, we present empirical evidence where time-varying loadings and volatilities in the dynamic Nelson-Siegel framework lead to significant increases in model fit. Improvements in the forecasting of the term structure are also reported. Finally, we provide an illustration where the model is applied to an unbalanced dataset. It shows that missing data entries can be estimated accurately.",
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Koopman, SJ, Mallee, MIP & van der Wel, M 2007 'Analyzing the Term Structure of Interest Rates using the Dynamic Nelson-Siegel Model with Time-Varying Parameters' Discussion paper TI, no. 07-095/4, Tinbergen Instituut, Amsterdam.

Analyzing the Term Structure of Interest Rates using the Dynamic Nelson-Siegel Model with Time-Varying Parameters. / Koopman, S.J.; Mallee, M.I.P.; van der Wel, M.

Amsterdam : Tinbergen Instituut, 2007. (Discussion paper TI; No. 07-095/4).

Research output: Working paperProfessional

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AB - 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 modelled by a vector autoregressive process. We propose to extend this framework in two directions. First, the factor loadings are made time-varying through a simple single step function and we show that the model fit increases significantly as a result. The step function can be replaced by a spline function to allow for more smoothness and flexibility. Second, we investigate empirically whether the volatility in interest rates across different time periods is constant. For this purpose, we introduce a common volatility component that is specified as a spline function of time and scaled appropriately for each series. Based on a data-set that is analysed by others, we present empirical evidence where time-varying loadings and volatilities in the dynamic Nelson-Siegel framework lead to significant increases in model fit. Improvements in the forecasting of the term structure are also reported. Finally, we provide an illustration where the model is applied to an unbalanced dataset. It shows that missing data entries can be estimated accurately.

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Koopman SJ, Mallee MIP, van der Wel M. Analyzing the Term Structure of Interest Rates using the Dynamic Nelson-Siegel Model with Time-Varying Parameters. Amsterdam: Tinbergen Instituut. 2007. (Discussion paper TI; 07-095/4).