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Maximum-likelihood estimation of fractional cointegration with application to the short end of the yield curve

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  • Michael J. Dueker
  • Richard Startz

Abstract

We estimate a multivariate autoregressive fractionally-integrated moving-average (ARFIMA) model to illustrate a cointegration testing methodology based on joint estimates of the fractional orders of integration of a cointegrating vector and its parent series. Although previous work has recognized that deviations from long-run relationships could exhibit long memory and go undetected in traditional 1(1)/i (0) cointegration analysis, previous tests for fractional cointegration relied on a two-step testing procedure and maintained the assumption in the second step that the parent series were known to have a unit root. In our example of fractional cointegration between 10-year government bond rates in the United States and Canada, we illustrate how uncertainty regarding the order of integration of the parent series can be even more important than uncertainty regarding the order of integration of the cointegrating vector when conducting a test for cointegration based on joint estimates. For this reason, the cointegration test based on joint estimates is less likely to reject the null of no cointegration and ought to have better size properties.

Suggested Citation

  • Michael J. Dueker & Richard Startz, 1997. "Maximum-likelihood estimation of fractional cointegration with application to the short end of the yield curve," Working Papers 1994-027, Federal Reserve Bank of St. Louis.
  • Handle: RePEc:fip:fedlwp:1994-027
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    References listed on IDEAS

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    1. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
    2. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    3. 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.
    4. Lo, Andrew W & MacKinlay, A Craig, 1990. "When Are Contrarian Profits Due to Stock Market Overreaction?," Review of Financial Studies, Society for Financial Studies, vol. 3(2), pages 175-205.
    5. Baillie, Richard T & Bollerslev, Tim, 1994. "The long memory of the forward premium," Journal of International Money and Finance, Elsevier, vol. 13(5), pages 565-571, October.
    6. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    7. 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.
    8. Cheung, Yin-Wong, 1993. "Long Memory in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 93-101, January.
    9. Sowell, Fallaw, 1992. "Modeling long-run behavior with the fractional ARIMA model," Journal of Monetary Economics, Elsevier, vol. 29(2), pages 277-302, April.
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    11. Granger, Clive W J, 1986. "Developments in the Study of Cointegrated Economic Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 213-228, August.
    12. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    13. 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.
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    Cited by:

    1. Valérie Mignon & Sandrine Lardic, 2003. "Cointégration fractionnaire entre la consommation et le revenu," Économie et Prévision, Programme National Persée, vol. 158(2), pages 123-142.

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    Keywords

    Cointegration ; Regression analysis;

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