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Testing for a Unit Root Against Fractional Alternatives in the Presence of a Maintained Trend

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  • Juan J. Dolado
  • Jesús Gonzalo
  • Laura Mayoral

Abstract

This paper discusses the role of deterministic components in the DGP and in the auxiliary regression model which underlies the implementation of the Fractional Dickey- Fuller (FDF) test for I(1) against F I(d) processes with d 2 [0; 1): Invariant tests to the presence of a drift under the null of I(1) are derived. In common with the standard DF approach in the I(1) vs: I(0) framework, we also examine the consequences of including a constant and /or a linear trend in the regression model when there is a drift under the null. A simple testing strategy entailing only asymptotically normally-distributed tests is proposed. Finally, an empirical application is provided where the FDF test allowing for deterministic components is used to test for long-memory in the per capita GDP of several OCDE countries.

Suggested Citation

  • Juan J. Dolado & Jesús Gonzalo & Laura Mayoral, 2003. "Testing for a Unit Root Against Fractional Alternatives in the Presence of a Maintained Trend," Working Papers 29, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:29
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    File URL: http://www.barcelonagse.eu/sites/default/files/working_paper_pdfs/29.pdf
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    References listed on IDEAS

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    1. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
    2. 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.
    3. Hylleberg, Svend & Mizon, Grayham E., 1989. "A note on the distribution of the least squares estimator of a random walk with drift," Economics Letters, Elsevier, vol. 29(3), pages 225-230.
    4. Laura Mayoral, 2003. "A New Minimum Distance Estimation Procedure of ARFIMA Processes," Working Papers 100, Barcelona School of Economics.
    5. Juan J. Dolado & Jesus Gonzalo & Laura Mayoral, 2002. "A Fractional Dickey-Fuller Test for Unit Roots," Econometrica, Econometric Society, vol. 70(5), pages 1963-2006, September.
    6. 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, June.
    7. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(4), pages 549-582, August.
    8. Ignacio N. Lobato & Carlos Velasco, 2006. "Optimal Fractional Dickey-Fuller tests," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 492-510, November.
    9. Diego Lubian, 1999. "Long‐Memory Errors in Time Series Regressions with a Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(5), pages 565-577, September.
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    Citations

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    Cited by:

    1. Laura Mayoral, 2005. "Is the observed persistence spurious? A test for fractional integration versus short memory and structural breaks," Economics Working Papers 956, Department of Economics and Business, Universitat Pompeu Fabra.
    2. María Dolores Gadea & Laura Mayoral, 2006. "The Persistence of Inflation in OECD Countries: A Fractionally Integrated Approach," International Journal of Central Banking, International Journal of Central Banking, vol. 2(1), March.
    3. Laura Mayoral, 2003. "Further Evidence on the Uncertain (Fractional) Unit Root in Real GNP," Working Papers 82, Barcelona School of Economics.

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