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Nonparametric Cointegration Analysis of Fractional Systems With Unknown Integration Orders

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Author Info
Morten Ørregaard Nielsen () (Queen's University and CREATES)

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Abstract

In this paper a nonparametric variance ratio testing approach is proposed for determining the cointegration rank in fractionally integrated systems. The test statistic is easily calculated without prior knowledge of the integration order of the data, the strength of the cointegrating relations, or the cointegration vector(s). The latter property makes it easier to implement than regression-based approaches, especially when examining relationships between several variables with possibly multiple cointegrating vectors. Since the test is nonparametric, it does not require the specification of a particular model and is invariant to short-run dynamics. Nor does it require the choice of any smoothing parameters that change the test statistic without being reflected in the asymptotic distribution. Furthermore, a consistent estimator of the cointegration space can be obtained from the procedure. The asymptotic distribution theory for the proposed test is non-standard but easily tabulated or simulated. Monte Carlo simulations demonstrate excellent finite sample properties, even rivaling those of well-specified parametric tests. The proposed methodology is applied to the term structure of interest rates, where, contrary to both fractional and integer-based parametric approaches, evidence in favor of the expectations hypothesis is found using the nonparametric approach.

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File URL: http://www.econ.queensu.ca/working_papers/papers/qed_wp_1174.pdf
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Publisher Info
Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1174.

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Length: 37 pages
Date of creation: Jul 2008
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Handle: RePEc:qed:wpaper:1174

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Related research
Keywords: cointegration rank; cointegration space; fractional integration and cointegration; interest rates; long memory; nonparametric; term structure; variance ratio;

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Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
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. Shintani, Mototsugu, 2001. "A simple cointegrating rank test without vector autoregression," Journal of Econometrics, Elsevier, vol. 105(2), pages 337-362, December. [Downloadable!] (restricted)
    Other versions:
  2. Breitung, Jorg & Taylor, A. M. Robert, 2003. "Corrigendum to "Nonparametric tests for unit roots and cointegration" [J. Econom. 108 (2002) 343-363]," Journal of Econometrics, Elsevier, vol. 117(2), pages 401-404, December. [Downloadable!] (restricted)
  3. Taylor, A. M. Robert, 2005. "Variance ratio tests of the seasonal unit root hypothesis," Journal of Econometrics, Elsevier, vol. 124(1), pages 33-54, January. [Downloadable!] (restricted)
  4. Breitung, Jorg & Hassler, Uwe, 2002. "Inference on the cointegration rank in fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 110(2), pages 167-185, October. [Downloadable!] (restricted)
    Other versions:
  5. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May. [Downloadable!] (restricted)
  6. Willa Chen & Clifford Hurvich, 2004. "Semiparametric Estimation of Fractional Cointegrating Subspaces," Econometrics 0412007, EconWPA. [Downloadable!]
  7. Javier Hualde & Peter M Robinson, 2003. "Cointegration in Fractional Systems with Unkown Integration Orders," STICERD - Econometrics Paper Series /2003/449, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  8. Katsumi Shimotsu, 2002. "Exact Local Whittle Estimation of Fractional Integration with Unknown Mean and Time Trend," Economics Discussion Papers 543, University of Essex, Department of Economics. [Downloadable!]
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  9. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1062-88, October. [Downloadable!] (restricted)
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  10. Snell, Andy, 1998. "Testing for r versus r-1 cointegrating vectors," Journal of Econometrics, Elsevier, vol. 88(1), pages 151-191, November. [Downloadable!] (restricted)
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  11. Søren Johansen & Morten Ørregaard Nielsen, 2007. "Likelihood inference for a nonstationary fractional autoregressive model," CREATES Research Papers 2007-33, School of Economics and Management, University of Aarhus. [Downloadable!]
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  12. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February. [Downloadable!] (restricted)
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  13. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November. [Downloadable!] (restricted)
  14. Bierens, Herman J., 1997. "Nonparametric cointegration analysis," Journal of Econometrics, Elsevier, vol. 77(2), pages 379-404, April. [Downloadable!] (restricted)
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  15. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254. [Downloadable!] (restricted)
  16. Pagan, A.R. & Hall, A.D. & Martin, V., 1995. "Modelling the Term Structure," Papers 284, Australian National University - Department of Economics.
  17. Morten Ørregaard Nielsen, 2008. "A Powerful Test of the Autoregressive Unit Root Hypothesis Based on a Tuning Parameter Free Statistic," CREATES Research Papers 2008-36, School of Economics and Management, University of Aarhus. [Downloadable!]
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  18. Engsted, Tom & Tanggaard, Carsten, 1994. "Cointegration and the US term structure," Journal of Banking & Finance, Elsevier, vol. 18(1), pages 167-181, January. [Downloadable!] (restricted)
  19. Harris, David, 1997. "Principal Components Analysis of Cointegrated Time Series," Econometric Theory, Cambridge University Press, vol. 13(04), pages 529-557, August. [Downloadable!]
  20. Hall, Anthony D & Anderson, Heather M & Granger, Clive W J, 1992. "A Cointegration Analysis of Treasury Bill Yields," The Review of Economics and Statistics, MIT Press, vol. 74(1), pages 116-26, February. [Downloadable!] (restricted)
  21. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June. [Downloadable!] (restricted)
  22. Chen, Willa W. & Hurvich, Clifford M., 2003. "Semiparametric Estimation of Multivariate Fractional Cointegration," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 629-642, January. [Downloadable!] (restricted)
  23. Phillips, P. C. B. & Ouliaris, S., 1988. "Testing for cointegration using principal components methods," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 205-230. [Downloadable!] (restricted)
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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. 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. [Downloadable!]
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