Skip to main content

Relationship Between Expected Treasury Bill and Eurodollar Interest Rates: A Fractional Cointegration Analysis

Abstract

In this paper, we extend Booth and Tse's (BT)1995 analysis of fractional cointegration between theexpected Eurodollar and Treasury bill interest ratesimplied by their respective futures contracts. Thedefinition of fractional cointegration suggested byCheung and Lai (1993) and used by BT is refined sothat it requires the cointegrating relationship to bestationary as well as mean-reverting. In addition tothe Geweke and Porter-Hudak method used by BT, a moreefficient Maximum Likelihood (ML) method is used toestimate the cointegrating relationship. The LM (Engle(1982)) test indicates the possible existence of aheteroscedastic cointegrating relationship. Therefore,we use heteroscedastic models (GARCH and ExponentialGARCH) to represent the cointegrating regressioninstead of the simple homoscedastic model used by BT.The empirical evidence cannot reject the nullhypothesis of a stationary fractional cointegrationrelationship between the Eurodollar and Treasury billinterest rates.

This is a preview of subscription content, access via your institution.

References

  • Baillie, R. T., “Long Memory Process and Fractional Integration in Econometrics.” Journal of Econometrics 73, 5–59, (1996).

    Google Scholar 

  • Baillie, R. T. and T. Bollerslev, “Cointegration, Fractional Cointegration, and Exchange Rate Dynamics.” Journal of Finance 49, 37–745, (1994).

    Google Scholar 

  • Bollerslev, T., R. Chou and K. Kroner, “ARCH Modeling in Finance: A Review of the Theory and Empirical Evidence.” Journal of Econometrics 52, 5–59, (1992).

    Google Scholar 

  • Booth, G. G. and Y. Tse, “Long Memory in Interest Rate Futures Markets: A Fractional Cointegration Analysis.” Journal of Futures Markets 15, 573–584, (1995).

    Google Scholar 

  • Cheung, Y. W. and K. S. Lai, “A Fractional Cointegration Analysis of Purchasing Power Parity.” Journal of Business & Economic Statistics 11, 103–112, (1993).

    Google Scholar 

  • Cosset, J.-C., “Forward Rates as Predictors of Future Interest Rates in the Eurocurrency Market.” Journal of International Business Studies, 71–83, (1982).

  • Dahlhaus, R., “Efficient Parameter Estimation for Self-similar Processes.” Annals of Statistics 17, 1749–1766, (1989).

    Google Scholar 

  • Dickey, D. A. and W. A. Fuller, “Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root.” Econometrica 49, 1057–1072, (1981).

    Google Scholar 

  • Diebold, F. X. and D. R. Glenn, “On the Power of Dickey-Fuller Tests against Fractional Alternatives.” Economics Letters 35, 155–160, (1991).

    Google Scholar 

  • Engle, R. F., “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation.” Econometrica 50, 987–1007, (1982).

    Google Scholar 

  • Engle, R. F. and C.W. J. Granger, “Cointegration and Error Correction: Representation, Estimation, and Testing.” Econometrica 55, 251–276, (1987).

    Google Scholar 

  • Fox, R. and M. S. Taqqu, “Large-sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series.” Annals of Statistics 14, 517–532, (1986).

    Google Scholar 

  • Fung, H. G. and S. C. Isberg, “The International Transmission of Eurodollar and US Interest Rates: A Cointegration Analysis.” Journal of Banking and Finance 16, 757–770, (1992).

    Google Scholar 

  • Fung, H.-G. and W. K. Leung, “The Pricing Relationship of Eurodollar Futures and Eurodollar Deposit Rates.” Journal of Futures Markets 13, 115–126, (1993).

    Google Scholar 

  • Fung, H. G. and W. C. Lo, “Memory in Interest Rate Futures.” The Journal of Futures Markets 13, 865–872, (1993).

    Google Scholar 

  • Fung, H. G. and W. C. Lo, “An Empirical Examination of the Ex Ante International Interest Rate Transmission.” Financial Review 30, 175–192, (1995).

    Google Scholar 

  • Geweke, J. F. and S. Porter-Hudak, “The Estimation and Application of Long Memory Time Series Models.” Journal of Time Series Analysis 1, 221–238, (1983).

    Google Scholar 

  • Granger, C. W. J. and R. Joyeux, “An Introduction to Long-Memory Time Series Models and Fractional Differenting.” Journal of Time Series Analysis 1, 15–39, (1980).

    Google Scholar 

  • Hartman, D. G., “The International Financial Market and US Interest Rates.” Journal of International Money and Finance 3, 91–103, (1984).

    Google Scholar 

  • Hedge, S. P. and B. MacDonald, “On the Informational Role of Treasury Bill Futures.” Journal of Futures Market 6, 629–643, (1986).

    Google Scholar 

  • Hendershott, P. H., “The Structure of International Interest Rates: The U.S. Treasury Bill Rate and the Eurodollar Deposit Rate.” Journal of Finance 22, 455–465, (1967).

    Google Scholar 

  • Hosking, J. R. M., “Fractional Differencing.” Biometrica 68, 165–176, (1981).

    Google Scholar 

  • Kaen, F. R. and G. A. Hachey, “Eurocurrency and National Money Market Interest Rates: An Empirical Investigation of Causality.” Journal of Money Credit and Banking 15, 327–338, (1983).

    Google Scholar 

  • Kwak, S., “The Structure of International Interest Rates: An Extension of Hendershott's Tests.” Journal of Finance 36, 897–900, (1971).

    Google Scholar 

  • Levin, J. H., “The Eurodollar Market and the International Transmission of Interest Rates.” Canadian Journal of Economics 7, 205–224, (1974).

    Google Scholar 

  • Lo, A. W., “Long Term Memory in Stock Market Prices.” Econometrica, 1279–1313, September, (1991).

  • Mandlebrot, B., “Statistical Methodology for Non-Periodic Cycles: From the Covariance to the R/S Analysis.” Annals of Economic and Social Measurement 1, 259–290, (1972).

    Google Scholar 

  • MacDonald, S. S. and S. Hein, “Futures Rates and Forward Rates as Predictors of Near-Term Treasury Bill Rates.” Journal of Futures Markets 3, 249–262, (1989).

    Google Scholar 

  • Nelson, D. B., “Conditional Heteroskedasticity in Asset Returns: A New Approach.” Econometrica 59, 347–370, (1991).

    Google Scholar 

  • Phillips, P. C. B. and P. Perron, “Testing Unit Roots in Time Series Regression.” Biometrica 75, 335–346, (1988).

    Google Scholar 

  • Schnitzel, P., “Causality in the Euro-Dollar Growth Process.” Quarterly Journal of Business and Economics 3, 66–77, (1983).

    Google Scholar 

  • Sowell, F., “The Fractional Unit Root Distribution.” Econometrica 58, 495–506, (1990).

    Google Scholar 

  • Swanson, P. E., “The International Transmission of Interest Rates: A Note on Causal Relationships Between Short Term External and Domestic US Dollar Returns.” Journal of Banking and Finance 12, 563–573, (1988).

    Google Scholar 

  • Walz, D. T. and R. W. Spencer, “The Information Content of Forward Rates: Further Evidence.” Journal of Financial Research 12, 69–81, (1989).

    Google Scholar 

  • Tse, Y. and G. Booth, “The Relationship Between U.S. and Eurodollar Interest Rates: Evidence from the Futures Market.” Weltwirschaftlches Archiv 131, 28–46, (1995).

    Google Scholar 

  • Tse, Y. and G. Booth, “Common Volatility Spillovers Between U.S. and Eurodollar Interest Rates: Evidence from the Futures Market.” Journal of Economics and Business 48, 299–312, (1996).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Shrestha, K., Welch, R.L. Relationship Between Expected Treasury Bill and Eurodollar Interest Rates: A Fractional Cointegration Analysis. Review of Quantitative Finance and Accounting 16, 65–80 (2001). https://doi.org/10.1023/A:1008340408261

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008340408261

Keywords

  • Interest Rate
  • Empirical Evidence
  • Future Contract
  • Treasury Bill
  • Cointegrating Relationship