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

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  • Tkacz Greg

    (Bank of Canada)

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.

Suggested Citation

  • Tkacz Greg, 2001. "Estimating the Fractional Order of Integration of Interest Rates Using a Wavelet OLS Estimator," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 5(1), pages 1-15, April.
    • Handle: RePEc:bpj:sndecm:v:5:y:2001:i:1:n:2
    DOI: 10.2202/1558-3708.1068
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    1. 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 167-181, March.
    2. David K. Backus & Stanley E. Zin, 1993. "Long-memory inflation uncertainty: evidence from the term structure of interest rates," Proceedings, Federal Reserve Bank of Cleveland, pages 681-708.
    3. 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.
    4. Mark J. Jensen, 1997. "Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long Memory Parameter," Econometrics 9710002, University Library of Munich, Germany.
    5. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    6. 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 555-576, June.
    7. Baillie, Richard T & Bollerslev, Tim, 1994. "Cointegration, Fractional Cointegration, and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 737-745, June.
    8. Diebold, Francis X & Gardeazabal, Javier & Yilmaz, Kamil, 1994. "On Cointegration and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 727-735, June.
    9. 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.
    10. 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 103-112, January.
    11. Dolado, Juan J & Jenkinson, Tim & Sosvilla-Rivero, Simon, 1990. "Cointegration and Unit Roots," Journal of Economic Surveys, Wiley Blackwell, vol. 4(3), pages 249-273.
    12. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    13. 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.
    14. Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
    15. William R. Parke, 1999. "What Is Fractional Integration?," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 632-638, November.
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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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