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

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  • Christensen, Bent Jesper
  • Kruse, Robinson
  • Sibbertsen, Philipp

Abstract

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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Bibliographic Info

Paper provided by Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät in its series Hannover Economic Papers (HEP) with number dp-519.

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Length: 33 pages
Date of creation: Oct 2013
Date of revision:
Handle: RePEc:han:dpaper:dp-519

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Keywords: Long memory; linear time series regression; Lagrange Multiplier test;

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  1. Pierre Perron & Tomoyoshi Yabu, 2005. "Testing for Shifts in Trend with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2005-026, Boston University - Department of Economics.
  2. 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.
  3. 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.
  4. 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.
  5. James Davidson & Nigar Hashimzade, 2007. "Representation and Weak Convergence of Stochastic Integrals with Fractional Integrator Processes," CREATES Research Papers 2007-45, School of Economics and Management, University of Aarhus.
  6. Michael Jansson & Morten Ørregaard Nielsen, 2009. "Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis," CREATES Research Papers 2009-37, School of Economics and Management, University of Aarhus.
  7. David I. Harvey & Stephen J. Leybourne, 2007. "Testing for time series linearity," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 149-165, 03.
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  9. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Simple, Robust, And Powerful Tests Of The Breaking Trend Hypothesis," Econometric Theory, Cambridge University Press, vol. 25(04), pages 995-1029, August.
  10. Christensen, Bent Jesper & Nielsen, Morten Orregaard, 2006. "Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting," Journal of Econometrics, Elsevier, vol. 133(1), pages 343-371, July.
  11. Søren Johansen & Morten Ørregaard Nielsen, 2012. "The role of initial values in nonstationary fractional time series models," Discussion Papers 12-18, University of Copenhagen. Department of Economics.
  12. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
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  14. 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.
  15. 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.
  16. Francesc Marmol & Juan J. Dolado, 1999. "Asymptotic Inference for Nonstationary Fractionally Integrated Processes," Computing in Economics and Finance 1999 513, Society for Computational Economics.
  17. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
  18. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2007. "Nonstationarity-extended local Whittle estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1353-1384, December.
  19. Peter M. Robinson & Javier Hualde, 2002. "Cointegration in Fractional Systems with Unknown Integration Orders," Faculty Working Papers 07/02, School of Economics and Business Administration, University of Navarra.
  20. Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
  21. 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.
  22. Iacone, Fabrizio & Leybourne, Stephen J. & Taylor, A.M. Robert, 2013. "ON THE BEHAVIOR OF FIXED-b TREND BREAK TESTS UNDER FRACTIONAL INTEGRATION," Econometric Theory, Cambridge University Press, vol. 29(02), pages 393-418, April.
  23. Nielsen M.O., 2004. "Optimal Residual-Based Tests for Fractional Cointegration and Exchange Rate Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 331-345, July.
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