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On Trend Breaks and Initial Condition in Unit Root Testing

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  • Anton Skrobotov

    (RANEPA)

Abstract

Recent approaches in unit root testing have taken into account the influences of initial condition, trend, and breaks in data using pre-testing and union of rejection testing strategies based on obtained information. This paper proposes an extension of the Harvey et al. (2012b) approach to address the case of uncertainty over the initial condition. It has been shown that this approach has low power under a large initial condition because it includes GLS-based tests. Therefore, the efficiency of some ADF-type unit root tests with breaks under various magnitudes of initial condition will be investigated, and new decision rules will be proposed. Additionally, the modifications of the proposed algorithm, using pre-testing for the trend co- efficient and the possible presence of multiple structural trend breaks, are also discussed. The asymptotic behaviors of all tests are analyzed under both a local-to-unity representation of the autoregressive root and a local-to-zero representation of trend and breaks magnitudes. The proposed tests show good asymptotic and finite sample properties under various magnitudes of nuisance parameters.

Suggested Citation

  • Anton Skrobotov, 2016. "On Trend Breaks and Initial Condition in Unit Root Testing," Working Papers 0097, Gaidar Institute for Economic Policy, revised 2016.
    • Handle: RePEc:gai:wpaper:0097
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    References listed on IDEAS

    as
    1. Carrion-i-Silvestre, Josep Lluís & Kim, Dukpa & Perron, Pierre, 2009. "Gls-Based Unit Root Tests With Multiple Structural Breaks Under Both The Null And The Alternative Hypotheses," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1754-1792, December.
    2. David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2010. "The impact of the initial condition on robust tests for a linear trend," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(4), pages 292-302, July.
    3. 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.
    4. 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(4), pages 995-1029, August.
    5. Mohitosh Kejriwal & Pierre Perron, 2010. "A sequential procedure to determine the number of breaks in trend with an integrated or stationary noise component," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 305-328, September.
    6. Cavaliere, Giuseppe & Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2011. "Testing For Unit Roots In The Presence Of A Possible Break In Trend And Nonstationary Volatility," Econometric Theory, Cambridge University Press, vol. 27(5), pages 957-991, October.
    7. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    8. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2012. "Testing for unit roots in the presence of uncertainty over both the trend and initial condition," Journal of Econometrics, Elsevier, vol. 169(2), pages 188-195.
    9. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2012. "Unit root testing under a local break in trend," Journal of Econometrics, Elsevier, vol. 167(1), pages 140-167.
    10. Busetti, Fabio & Harvey, Andrew, 2008. "Testing For Trend," Econometric Theory, Cambridge University Press, vol. 24(1), pages 72-87, February.
    11. Elliott, Graham, 1999. "Efficient Tests for a Unit Root When the Initial Observation Is Drawn from Its Unconditional Distribution," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 767-783, August.
    12. Vogelsang, Timothy J & Perron, Pierre, 1998. "Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1073-1100, November.
    13. 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(3), pages 587-636, June.
    14. David I. Harvey & Stephen J. Leybourne, 2006. "Power of a Unit‐Root Test and the Initial Condition," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 739-752, September.
    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.
    16. David I. Harvey & Stephen J. Leybourne & A.M. Robert Taylor, 2014. "Unit Root Testing under a Local Break in Trend using Partial Information on the Break Date," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(1), pages 93-111, February.
    17. 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.
    18. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    19. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    20. 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.
    21. Kim, Dukpa & Perron, Pierre, 2009. "Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses," Journal of Econometrics, Elsevier, vol. 148(1), pages 1-13, January.
    22. 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.
    23. David I. Harvey & Stephen J. Leybourne, 2014. "Break Date Estimation for Models with Deterministic Structural Change," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(5), pages 623-642, October.
    24. Hui Liu & Gabriel Rodríguez, 2006. "Unit root tests and structural change when the initial observation is drawn from its unconditional distribution," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 225-251, July.
    25. 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.
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    Cited by:

    1. Skrobotov, Anton, 2020. "Survey on structural breaks and unit root tests," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 58, pages 96-141.
    2. Meligkotsidou, Loukia & Tzavalis, Elias & Vrontos, Ioannis, 2017. "On Bayesian analysis and unit root testing for autoregressive models in the presence of multiple structural breaks," Econometrics and Statistics, Elsevier, vol. 4(C), pages 70-90.

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    More about this item

    Keywords

    unit root test; infimum Dickey-Fuller tests; local trend; local trend break; asymptotic local power; union of rejection; pre-testing; multiple breaks in trend.;
    All these keywords.

    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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