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Variance Ratio Testing for Fractional Cointegration in Presence of Trends and Trend Breaks

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  • Dechert, Andreas

Abstract

Modeling fractional cointegration relationships has become a major topic in applied time series analysis as it steps back from the traditional rigid I(1)/I(0) methodology. Hence, the number of proposed tests and approaches has grown over the last decade. The aim of this paper is to study the nonparametric variance ratio approach suggested by Nielsen for the case of fractional cointegration in presence of linear trend and trend breaks. The consideration of trend breaks is very important in order to avoid spurious fractional integration, so this possibility should be regarded by practitioners. This paper proposes to calculate p-values by means of gamma distributions and gives response regressions parameters for the asymptotic moments of them. In Monte Carlo simulations this work compares the power of the approach against a Johansen type rank test suggested, which is robust against trend breaks but not fractional (co-)integration. As the approach also obtains an estimator for the cointegration space, the paper compares it with OLS estimates in simulations. As an empirical example the validity of the market expectation hypothesis is tested for monthly Treasury bill rates ranging from 1958-2011, which might have a trend break around September 1979 due to change of American monetary policy.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 41044.

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Date of creation: 04 Sep 2012
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Handle: RePEc:pra:mprapa:41044

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Keywords: fractional integration; fractional cointegration; long memory; variance ratio; nonparametric; trend breaks; market expectation hypothesis;

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  1. Katsumi Shimotsu, 2002. "Exact Local Whittle Estimation of Fractional Integration with Unknown Mean and Time Trend," Economics Discussion Papers, University of Essex, Department of Economics 543, University of Essex, Department of Economics.
  2. Joerg Breitung and Uwe Hassler, 2001. "Inference on the Cointegration Rank in Fractionally Integrated Processes," Computing in Economics and Finance 2001, Society for Computational Economics 233, Society for Computational Economics.
  3. Søren Johansen & Rocco Mosconi & Bent Nielsen, 2000. "Cointegration analysis in the presence of structural breaks in the deterministic trend," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 3(2), pages 216-249.
  4. Shimotsu, Katsumi & Phillips, Peter C.B., 2006. "Local Whittle estimation of fractional integration and some of its variants," Journal of Econometrics, Elsevier, Elsevier, vol. 130(2), pages 209-233, February.
  5. 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.
  6. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, Elsevier, vol. 106(2), pages 217-241, February.
  7. Søren Johansen & Morten Ørregaard Nielsen, 2010. "Likelihood inference for a fractionally cointegrated vector autoregressive model," CREATES Research Papers 2010-24, School of Economics and Management, University of Aarhus.
  8. Engsted, Tom & Tanggaard, Carsten, 1994. "Cointegration and the US term structure," Journal of Banking & Finance, Elsevier, Elsevier, vol. 18(1), pages 167-181, January.
  9. Nielsen, Morten Orregaard & Shimotsu, Katsumi, 2007. "Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach," Journal of Econometrics, Elsevier, Elsevier, vol. 141(2), pages 574-596, December.
  10. Morten Ørregaard Nielsen, 2009. "Nonparametric Cointegration Analysis of Fractional Systems With Unknown Integration Orders," CREATES Research Papers 2009-02, School of Economics and Management, University of Aarhus.
  11. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 95(5), pages 1062-88, October.
  12. 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.
  13. Johansen, SØren, 2008. "A Representation Theory For A Class Of Vector Autoregressive Models For Fractional Processes," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 24(03), pages 651-676, June.
  14. Jurgen A. Doornik, 1998. "Approximations To The Asymptotic Distributions Of Cointegration Tests," Journal of Economic Surveys, Wiley Blackwell, Wiley Blackwell, vol. 12(5), pages 573-593, December.
  15. Fabrizio Iacone, 2009. "A Semiparametric Analysis of the Term Structure of the US Interest Rates," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(4), pages 475-490, 08.
  16. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, Econometric Society, vol. 55(2), pages 251-76, March.
  17. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, Econometric Society, vol. 57(6), pages 1361-1401, November.
  18. Phillips, P. C. B. & Ouliaris, S., 1988. "Testing for cointegration using principal components methods," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 12(2-3), pages 205-230.
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