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Stationarity and the term structure of interest rates: a characterisation of stationary and unit root yield curves

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Clive G. Bowsher
Roland Meeks

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Abstract

The nature of yield curve dynamics and the determinants of the integration order of yields are investigated using a benchmark economy in which the logarithmic expectations theory holds and the regularity condition of a limiting yield and limiting term premium is satisfied. By considering a zero-coupon yield curve with a complete term structure of maturities, a linear vector autoregressive process is constructed that provides an arbitrarily accurate moving average representation of the complete yield curve as its cross-sectional dimension (n) goes to infinity. We use this to prove the following novel results. First, any I(2) component vanishes owing to the almost sure (a.s.) convergence of the innovations to yields, vt(n), as n. Second, the yield curve is stationary if and only if nvt(n) converges a.s., or equivalently the innovations to log discount bond prices converge a.s.; otherwise yields are I(1). A necessary condition for either stationarity or the absence of arbitrage is that the limiting yield is constant over time. Since the time-varying component of term premia is small in various fixed-income markets, these results provide insight into the critical determinants of the stationarity properties of the term structure.

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Paper provided by Federal Reserve Bank of Dallas in its series Working Papers with number 0811.

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Date of creation: 2008
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Handle: RePEc:fip:feddwp:0811

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Keywords: Econometric models ; Interest rates;

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  3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November. [Downloadable!] (restricted)
  4. Dahlquist, Magnus & Jonsson, Gunnar, 1995. "The information in Swedish short-maturity forward rates," European Economic Review, Elsevier, vol. 39(6), pages 1115-1131, June. [Downloadable!] (restricted)
  5. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January. [Downloadable!] (restricted)
  6. Dybvig, Philip H & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1996. "Long Forward and Zero-Coupon Rates Can Never Fall," Journal of Business, University of Chicago Press, vol. 69(1), pages 1-25, January. [Downloadable!] (restricted)
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  7. Bekaert, Geert & Hodrick, Robert J. & Marshall, David A., 2001. "Peso problem explanations for term structure anomalies," Journal of Monetary Economics, Elsevier, vol. 48(2), pages 241-270, October. [Downloadable!] (restricted)
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  8. John H. Cochrane & Monika Piazzesi, 2005. "Bond Risk Premia," American Economic Review, American Economic Association, vol. 95(1), pages 138-160, March. [Downloadable!]
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  9. Nicolau, Jo o, 2002. "Stationary Processes That Look Like Random Walks The Bounded Random Walk Process In Discrete And Continuous Time," Econometric Theory, Cambridge University Press, vol. 18(01), pages 99-118, February. [Downloadable!]
  10. Lanne, Markku & Saikkonen, Pentti, 2002. "Threshold Autoregressions for Strongly Autocorrelated Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 282-89, April.
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  11. Geert Bekaert, 2001. "Expectations Hypotheses Tests," Journal of Finance, American Finance Association, vol. 56(4), pages 1357-1394, 08. [Downloadable!] (restricted)
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  12. Campbell, John Y & Shiller, Robert J, 1991. "Yield Spreads and Interest Rate Movements: A Bird's Eye View," Review of Economic Studies, Blackwell Publishing, vol. 58(3), pages 495-514, May. [Downloadable!] (restricted)
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  13. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1062-88, October. [Downloadable!] (restricted)
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  14. Hardouvelis, Gikas A., 1994. "The term structure spread and future changes in long and short rates in the G7 countries: Is there a puzzle?," Journal of Monetary Economics, Elsevier, vol. 33(2), pages 255-283, April. [Downloadable!] (restricted)
  15. Francis A. Longstaff, 2000. "Arbitrage and the Expectations Hypothesis," Journal of Finance, American Finance Association, vol. 55(2), pages 989-994, 04. [Downloadable!] (restricted)
  16. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1981. "A Re-examination of Traditional Hypotheses about the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 36(4), pages 769-99, September. [Downloadable!] (restricted)
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