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A unified framework for testing in the linear regression model under unknown order of fractional integration

  • Bent Jesper Christensen

    ()

    (Aarhus University and CREATES)

  • Robinson Kruse

    ()

    (Leibniz University Hannover and CREATES)

  • Philipp Sibbertsen

    ()

    (Leibniz University Hannover)

We consider hypothesis testing in a general linear time series regression framework when the possibly fractional order of integration of the error term is unknown. We show that the approach suggested by Vogelsang (1998a) for the case of integer integration does not apply to the case of fractional integration. We propose a Lagrange Multiplier-type test whose limiting distribution is independent of the order of integration of the errors. Different testing scenarios for the case of deterministic and stochastic regressors are considered. Simulations demonstrate that the proposed test works well for a variety of different cases, thereby emphasizing its generality.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2013-35.

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Length: 33
Date of creation: 05 2013
Date of revision:
Handle: RePEc:aah:create:2013-35
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. Shimotsu, Katsumi, 2010. "Exact Local Whittle Estimation Of Fractional Integration With Unknown Mean And Time Trend," Econometric Theory, Cambridge University Press, vol. 26(02), pages 501-540, April.
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  5. James Davidson & Nigar Hashimzade, 2008. "Representation and Weak Convergence of Stochastic Integrals with Fractional Integrator Processes," Discussion Papers 0807, Exeter University, Department of Economics.
  6. Iacone, Fabrizio & Leybourne, Stephen J. & Robert Taylor, A.M., 2013. "Testing for a break in trend when the order of integration is unknown," Journal of Econometrics, Elsevier, vol. 176(1), pages 30-45.
  7. Michael Jansson & Morten Ørregaard Nielsen, 2009. "Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis," Working Papers 1213, Queen's University, Department of Economics.
  8. Peter C.B. Phillips, 1988. "Optimal Inference in Cointegrated Systems," Cowles Foundation Discussion Papers 866R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
  9. Bent Jesper Christensen & Morten Ø. Nielsen, . "Semiparametric Analysis of Stationary Fractional Cointegration and the Implied-Realized Volatility Relation in High-Frequency Options Data," Economics Working Papers 2001-4, School of Economics and Management, University of Aarhus.
  10. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  11. Eduardo Zambrano & Timothy J. Vogelsang, 2000. "A Simple Test of the Law of Demand for the United States," Econometrica, Econometric Society, vol. 68(4), pages 1013-1022, July.
  12. Fabrizio Iacone & Stephen J. Leybourne & A. M. Robert Taylor, 2011. "On the behaviour of fixed-b trend break tests under fractional integration," Discussion Papers 11/03, University of Nottingham, Granger Centre for Time Series Econometrics.
  13. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Testing for Shifts in Trend With an Integrated or Stationary Noise Component," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 369-396.
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  16. Juan J. Dolado & Francesc Marmol, 2004. "Asymptotic inference results for multivariate long-memory processes," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 168-190, 06.
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  18. 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.
  19. Morten Oerregaard Nielsen, . "Optimal Residual Based Tests for Fractional Cointegration and Exchange Rate Dynamics," Economics Working Papers 2002-7, School of Economics and Management, University of Aarhus.
  20. Vogelsang, Timothy J, 1998. "Testing for a Shift in Mean without Having to Estimate Serial-Correlation Parameters," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(1), pages 73-80, January.
  21. David I. Harvey & Stephen J. Leybourne & Lisa Xiao, 2010. "Testing for nonlinear deterministic components when the order of integration is unknown," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 379-391, 09.
  22. Nielsen, Morten Orregaard, 2007. "Local Whittle Analysis of Stationary Fractional Cointegration and the ImpliedRealized Volatility Relation," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 427-446, October.
  23. Francesc Marmol & Juan J. Dolado, 1999. "Asymptotic Inference for Nonstationary Fractionally Integrated Processes," Computing in Economics and Finance 1999 513, Society for Computational Economics.
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