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Estimating the Fractional Order of Integration of Interest Rates Using a Wavelet OLS Estimator

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Author Info
Greg Tkacz (Bank of Canada)

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Abstract

The debate on the order of integration of interest rates has long focused on the I(1) versus I(0) distinction. In this paper we instead use the wavelet OLS estimator of Jensen (1999) to estimate the fractional integration parameters of several interest rates for the United States and Canada from 1948 to 1999. We find that most rates are mean-reverting in the very long run, with the fractional order of integration increasing with the term to maturity. The speeds of mean reversion are lower in Canada, likely because of a positive country-specific risk premium. We also demonstrate that interest rate yield spreads involve noticeable persistence, indicating that these are also not strict I(0) processes. One consequence of these findings is that shocks to most interest rates and their spreads are very long lasting, yet not necessarily infinite.

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Publisher Info
Article provided by Berkeley Electronic Press in its journal Studies in Nonlinear Dynamics & Econometrics.

Volume (Year): 5 (2001)
Issue (Month): 1 ()
Pages: 1068-1068
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Handle: RePEc:bep:sndecm:5:2001:1:1068-1068

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Keywords: fractional integration interest rates wavelets

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References listed on IDEAS
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  1. Estrella, Arturo & Hardouvelis, Gikas A, 1991. " The Term Structure as a Predictor of Real Economic Activity," Journal of Finance, American Finance Association, vol. 46(2), pages 555-76, June. [Downloadable!] (restricted)
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  2. Diebold, Francis X & Gardeazabal, Javier & Yilmaz, Kamil, 1994. " On Cointegration and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 727-35, June. [Downloadable!] (restricted)
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  3. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November. [Downloadable!] (restricted)
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  4. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March. [Downloadable!] (restricted)
  5. Baillie, Richard T & Bollerslev, Tim, 1989. " Common Stochastic Trends in a System of Exchange Rates," Journal of Finance, American Finance Association, vol. 44(1), pages 167-81, March. [Downloadable!] (restricted)
  6. Diebold, Francis X. & Rudebusch, Glenn D., 1991. "On the power of Dickey-Fuller tests against fractional alternatives," Economics Letters, Elsevier, vol. 35(2), pages 155-160, February. [Downloadable!] (restricted)
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  7. Baillie, Richard T & Bollerslev, Tim, 1994. " Cointegration, Fractional Cointegration, and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 737-45, June. [Downloadable!] (restricted)
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  8. Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March. [Downloadable!] (restricted)
  9. Cheung, Yin-Wong & Lai, Kon S, 1993. "A Fractional Cointegration Analysis of Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 103-12, January.
  10. David K. Backus & Stanley E. Zin, 1993. "Long-memory Inflation Uncertainty: Evidence from the Term Structure of Interest Rates," NBER Technical Working Papers 0133, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  11. William R. Parke, 1999. "What Is Fractional Integration?," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 632-638, November. [Downloadable!] (restricted)
  12. Pfann, Gerard A. & Schotman, Peter C. & Tschernig, Rolf, 1996. "Nonlinear interest rate dynamics and implications for the term structure," Journal of Econometrics, Elsevier, vol. 74(1), pages 149-176, September. [Downloadable!] (restricted)
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  13. Dolado, Juan J & Jenkinson, Tim & Sosvilla-Rivero, Simon, 1990. " Cointegration and Unit Roots," Journal of Economic Surveys, Blackwell Publishing, vol. 4(3), pages 249-73.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Vuorenmaa , Tommi, 2005. "A wavelet analysis of scaling laws and long-memory in stock market volatility," Research Discussion Papers 27/2005, Bank of Finland. [Downloadable!]
  2. Patrick Crowley, 2005. "An intuitive guide to wavelets for economists," Econometrics 0503017, EconWPA. [Downloadable!]
    Other versions:
  3. Ozun, Alper & Cifter, Atilla, 2007. "Modeling Long-Term Memory Effect in Stock Prices: A Comparative Analysis with GPH Test and Daubechies Wavelets," MPRA Paper 2481, University Library of Munich, Germany. [Downloadable!]
  4. Jan Beran & Dirk Ocker, 2002. "Pricing of cap-interest rates based on renewal processes," CoFE Discussion Paper 02-10, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
  5. Laurini, Márcio P. & Hotta, Luiz K., 2008. "Inferência indireta em modelos fracionários de taxas de juros de curto prazo," Ibmec Working Papers wpe_119, Ibmec Working Paper, Ibmec São Paulo. [Downloadable!]
  6. Luis A. Gil-Alana, 2003. "Strong dependence in the real interest rates," Applied Economics, Taylor and Francis Journals, vol. 35(2), pages 119-124, January. [Downloadable!] (restricted)
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