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

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  • Tkacz, Greg

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 use instead 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, due likely to a positive country-specific risk premium. We also demonstrate that yield spreads contain noticeable persistence, indicating that these are also not strict I(0) processes. The consequences of these findings are that shocks to most interest rates and their spreads are very long-lasting, yet not necessarily infinite.

Suggested Citation

  • Tkacz, Greg, 2000. "Estimating the Fractional Order of Integration of Interest Rates Using a Wavelet OLS Estimator," Staff Working Papers 00-5, Bank of Canada.
  • Handle: RePEc:bca:bocawp:00-5
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    Cited by:

    1. Matthew Greenwood-Nimmo & Youngcheol Shin, 2011. "Shifting Preferences at the Fed: Evidence from Rolling Dynamic Multipliers and Impulse Response Analysis," Working Papers 2011-057, Madras School of Economics,Chennai,India.
    2. Coleman, Simeon & Sirichand, Kavita, 2012. "Fractional integration and the volatility of UK interest rates," Economics Letters, Elsevier, vol. 116(3), pages 381-384.
    3. Daniel Agyapong, 2014. "Stock Market Integration in West African Monetary Zone: A Linear and Nonlinear Cointegration Approach," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 4(5), pages 563-587, May.
    4. Esben Hoeg & Per Frederiksen, 2006. "The Fractional OU Process: Term Structure Theory and Application," Computing in Economics and Finance 2006 194, Society for Computational Economics.
    5. Jin, Hyun J. & Elder, John & Koo, Won W., 2006. "A reexamination of fractional integrating dynamics in foreign currency markets," International Review of Economics & Finance, Elsevier, vol. 15(1), pages 120-135.
    6. Khan, Hashmat, 2000. "Price Stickiness, Inflation, and Output Dynamics: A Cross-Country Analysis," Staff Working Papers 00-13, Bank of Canada.
    7. Høg, Esben & Frederiksen, Per & Schiemert, Daniel, 2008. "On the Generalized Brownian Motion and its Applications in Finance," Finance Research Group Working Papers F-2008-07, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    8. Cifter, Atilla & Yilmazer, Sait & Cifter, Elif, 2009. "Analysis of sectoral credit default cycle dependency with wavelet networks: Evidence from Turkey," Economic Modelling, Elsevier, vol. 26(6), pages 1382-1388, November.
    9. Alper Ozun & Atilla Cifter, 2008. "Modeling long-term memory effect in stock prices: A comparative analysis with GPH test and Daubechies wavelets," Studies in Economics and Finance, Emerald Group Publishing, vol. 25(1), pages 38-48, March.
    10. Laurini, Márcio Poletti & Hotta, Luiz Koodi, 2013. "Indirect Inference in fractional short-term interest rate diffusions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 109-126.
    11. Høg, Espen P. & Frederiksen, Per H., 2006. "The Fractional Ornstein-Uhlenbeck Process: Term Structure Theory and Application," Finance Research Group Working Papers F-2006-01, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    12. Adam Golinski & Peter Spencer, 2012. "The Meiselman forward interest rate revision regression as an Affine Term Structure Model," Discussion Papers 12/27, Department of Economics, University of York.
    13. Alagidede, Paul & Coleman, Simeon & Cuestas, Juan Carlos, 2012. "Inflationary shocks and common economic trends: Implications for West African monetary union membership," Journal of Policy Modeling, Elsevier, vol. 34(3), pages 460-475.
    14. In, Francis & Kim, Sangbae, 2006. "Multiscale hedge ratio between the Australian stock and futures markets: Evidence from wavelet analysis," Journal of Multinational Financial Management, Elsevier, vol. 16(4), pages 411-423, October.
    15. Gil-Alana, Luis A., 2004. "Modelling the U.S. interest rate in terms of I(d) statistical models," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(4), pages 475-486, September.
    16. Coleman, Simeon, 2012. "Where Does the Axe Fall? Inflation Dynamics and Poverty Rates: Regional and Sectoral Evidence for Ghana," World Development, Elsevier, vol. 40(12), pages 2454-2467.
    17. Luis Gil-Alana, 2003. "Strong dependence in the real interest rates," Applied Economics, Taylor & Francis Journals, vol. 35(2), pages 119-124.

    More about this item

    Keywords

    Econometric and statistical methods; Interest rates;

    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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