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An Unobserved Components Model of the Yield Curve

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  • RICHARD STARTZ
  • KWOK PING TSANG

Abstract

We develop an unobserved component model in which the short‐term interest rate is composed of a stochastic trend and a stationary cycle. Using the Nelson–Siegel model of the yield curve as inspiration, we estimate an extremely parsimonious state‐space model of interest rates across time and maturity. The time‐series process suggests a specific functional form for the yield curve. We use the Kalman filter to estimate the time‐series process jointly with observed yield curves, greatly improving empirical identification. Our stochastic process generates a three‐factor model for the term structure. At the estimated parameters, trend and slope factors matter while the third factor is empirically unimportant. Our baseline model fits the yield curve well. Model generated estimates of uncertainty are positively correlated with estimated term premia. An extension of the model with regime switching identifies a high‐variance regime and a low‐variance regime, where the high‐variance regime occurs rarely after the mid‐1980s. The term premium is higher, and more so for yields of short maturities, in the high‐variance regime than in the low‐variance regime. The estimation results support our model as a simple and yet reliable framework for modeling the term structure.

Suggested Citation

  • Richard Startz & Kwok Ping Tsang, 2010. "An Unobserved Components Model of the Yield Curve," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(8), pages 1613-1640, December.
    • Handle: RePEc:wly:jmoncb:v:42:y:2010:i:8:p:1613-1640
    DOI: 10.1111/j.1538-4616.2010.00356.x
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    1. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February.
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    1. Trenkler, Carsten & Weber, Enzo, 2016. "On the identification of multivariate correlated unobserved components models," Economics Letters, Elsevier, vol. 138(C), pages 15-18.
    2. Soloschenko, Max & Weber, Enzo, 2014. "Capturing the Interaction of Trend, Cycle, Expectations and Risk Premia in the US Term Structure," University of Regensburg Working Papers in Business, Economics and Management Information Systems 475, University of Regensburg, Department of Economics.
    3. Massimo Guidolin & Manuela Pedio, 2019. "Forecasting and Trading Monetary Policy Effects on the Riskless Yield Curve with Regime Switching Nelson†Siegel Models," Working Papers 639, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    4. Levant, Jared & Ma, Jun, 2017. "A dynamic Nelson-Siegel yield curve model with Markov switching," Economic Modelling, Elsevier, vol. 67(C), pages 73-87.
    5. Massimo Guidolin & Manuela Pedio, 2019. "Forecasting and Trading Monetary Policy Switching Nelson-Siegel Models," BAFFI CAREFIN Working Papers 19106, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    6. Levant, Jared & Ma, Jun, 2016. "Investigating United Kingdom's monetary policy with Macro-Factor Augmented Dynamic Nelson–Siegel models," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 117-127.
    7. Xiaojing Xi & Rogemar Mamon, 2014. "Capturing the Regime-Switching and Memory Properties of Interest Rates," Computational Economics, Springer;Society for Computational Economics, vol. 44(3), pages 307-337, October.

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