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Double Unit Roots Testing, GLS-detrending and Uncertainty over the Initial Conditions

Author

Listed:
  • Anton Skrobotov

    (Gaidar Institute for Economic Policy)

Abstract

This paper proposes the extension of the Hasza and Fuller (1979) test for double unit roots based on GLS-detrending. The limiting distribution of this test is obtained under local to unity representation and coincides with the distribution of the conventional test in the absence of a deterministic component. The proposed test has both better asymptotic and _nite sample properties in comparison to tests based on OLS-detrending. This paper proposes modi_ed information criteria for the implementation of the proposed test for double unit roots in _nite samples in which an additional term is incorporated into the penalty function. This provides better size control under various data generating processes, especially for strongly negative moving average components. This paper also analyzes the power behavior of tests under non-negligible initial conditions and proposes union of rejection testing strategy of three tests following the Harvey et al. (2009) approach. This strategy is more robust across various magnitudes of the initial conditions and eliminates large power losses that occur due to the use of only one of the tests.

Suggested Citation

  • Anton Skrobotov, 2013. "Double Unit Roots Testing, GLS-detrending and Uncertainty over the Initial Conditions," Working Papers 0083, Gaidar Institute for Economic Policy, revised 2013.
  • Handle: RePEc:gai:wpaper:0083
    as

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    File URL: http://www.iep.ru/files/RePEc/gai/wpaper/0083Skrobotov.pdf
    File Function: Revised version, 2013
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    References listed on IDEAS

    as
    1. Peter C.B. Phillips & Shu-Ping Shi & Jun Yu, 2011. "Testing for Multiple Bubbles," Working Papers 09-2011, Singapore Management University, School of Economics.
    2. Sen, D L & Dickey, David A, 1987. "Symmetric Test for Second Differencing in Univariate Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 463-473, October.
    3. Niels Haldrup & Peter Lildholdt, 2005. "Local power functions of tests for double unit roots," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(2), pages 159-179.
    4. Elliott, Graham & Muller, Ulrich K., 2006. "Minimizing the impact of the initial condition on testing for unit roots," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 285-310.
    5. Perron, Pierre & Qu, Zhongjun, 2007. "A simple modification to improve the finite sample properties of Ng and Perron's unit root tests," Economics Letters, Elsevier, vol. 94(1), pages 12-19, January.
    6. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    7. Nabeya, Seiji & Perron, Pierre, 1994. "Local asymptotic distribution related to the AR(1) model with dependent errors," Journal of Econometrics, Elsevier, vol. 62(2), pages 229-264, June.
    8. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    9. Shin, Dong Wan & Kim, Hyun Jung, 1999. "Semiparametric Tests for Double Unit Roots Based on Symmetric Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 67-73, January.
    10. Harvey, David I. & Leybourne, Stephen J., 2014. "Asymptotic behaviour of tests for a unit root against an explosive alternative," Economics Letters, Elsevier, vol. 122(1), pages 64-68.
    11. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, July.
    12. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition," Econometric Theory, Cambridge University Press, vol. 25(03), pages 587-636, June.
    13. Dickey, David A & Pantula, Sastry G, 1987. "Determining the Ordering of Differencing in Autoregressive Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 455-461, October.
    14. Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2004. "On Tests For Double Differencing: Methods Of Demeaning And Detrending And The Role Of Initial Values," Econometric Theory, Cambridge University Press, vol. 20(01), pages 95-115, February.
    15. David I. Harvey & Stephen J. Leybourne, 2005. "On testing for unit roots and the initial observation," Econometrics Journal, Royal Economic Society, vol. 8(1), pages 97-111, March.
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    More about this item

    Keywords

    Double unit roots test; GLS-detrending; lag length selection; information criteria; uncertainty over the initial conditions; union of rejection;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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