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Bootstrap Unit-Root Tests: Comparison and Extensions

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  • Franz C. Palm
  • Stephan Smeekes
  • Jean-Pierre Urbain

Abstract

In this article, we study and compare the properties of several bootstrap unit-root tests recently proposed in the literature. The tests are Dickey-Fuller (DF) or Augmented DF, based either on residuals from an autoregression and the use of the block bootstrap or on first-differenced data and the use of the stationary bootstrap or sieve bootstrap. We extend the analysis by interchanging the data transformations (differences vs. residuals), the types of bootstrap and the presence or absence of a correction for autocorrelation in the tests. Copyright 2008 The Authors

Suggested Citation

  • Franz C. Palm & Stephan Smeekes & Jean-Pierre Urbain, 2008. "Bootstrap Unit-Root Tests: Comparison and Extensions," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 371-401, March.
  • Handle: RePEc:bla:jtsera:v:29:y:2008:i:2:p:371-401
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    References listed on IDEAS

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    1. Paparoditis, Efstathios & Politis, Dimitris N, 2001. "Unit Root Testing via the Continuous-Path Block Bootstrap," University of California at San Diego, Economics Working Paper Series qt9qb4r775, Department of Economics, UC San Diego.
    2. 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.
    3. Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(02), pages 469-490, April.
    4. Anders Rygh Swensen, 2003. "Bootstrapping unit root tests for integrated processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 99-126, January.
    5. Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, May.
    6. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, July.
    7. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    8. Swensen, Anders Rygh, 2003. "A Note On The Power Of Bootstrap Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(01), pages 32-48, February.
    9. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
    10. Parker, Cameron & Paparoditis, Efstathios & Politis, Dimitris N., 2006. "Unit root testing via the stationary bootstrap," Journal of Econometrics, Elsevier, vol. 133(2), pages 601-638, August.
    11. Paparoditis, Efstathios & Politis, Dimitris N., 2005. "Bootstrapping Unit Root Tests for Autoregressive Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 545-553, June.
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    Cited by:

    1. Shin, Dong Wan & Hwang, Eunju, 2013. "Stationary bootstrapping for cointegrating regressions," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 474-480.
    2. Richard, Patrick, 2009. "Modified fast double sieve bootstraps for ADF tests," Computational Statistics & Data Analysis, Elsevier, pages 4490-4499.
    3. Xuguang Sheng & Jingyun Yang, 2013. "Truncated Product Methods for Panel Unit Root Tests," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 75(4), pages 624-636, August.
    4. Smeekes S. & Urbain J.R.Y.J., 2014. "A multivariate invariance principle for modified wild bootstrap methods with an application to unit root testing," Research Memorandum 008, Maastricht University, Graduate School of Business and Economics (GSBE).
    5. repec:gam:jecnmx:v:4:y:2016:i:2:p:21:d:67747 is not listed on IDEAS
    6. Smeekes, Stephan & Taylor, A.M. Robert, 2012. "Bootstrap Union Tests For Unit Roots In The Presence Of Nonstationary Volatility," Econometric Theory, Cambridge University Press, pages 422-456.
    7. Hwang, Eunju & Shin, Dong Wan, 2015. "Stationary bootstrapping for semiparametric panel unit root tests," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 14-25.
    8. Jaap W. B. Bos & Bertrand Candelon & Claire Economidou, 2016. "Does knowledge spill over across borders and technology regimes?," Journal of Productivity Analysis, Springer, vol. 46(1), pages 63-82, August.
    9. Stephan Smeekes, 2013. "Detrending Bootstrap Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 869-891, November.
    10. Guodong Li & Chenlei Leng & Chih-Ling Tsai, 2014. "A Hybrid Bootstrap Approach To Unit Root Tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(4), pages 299-321, July.
    11. V. A. Reisen & C. Lévy-Leduc & M. Bourguignon & H. Boistard, 2017. "Robust Dickey–Fuller tests based on ranks for time series with additive outliers," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(1), pages 115-131, January.
    12. Gutierrez, Luciano, 2011. "Bootstrapping asset price bubbles," Economic Modelling, Elsevier, vol. 28(6), pages 2488-2493.
    13. Stephan Smeekes & Jean-Pierre Urbain, 2014. "On the Applicability of the Sieve Bootstrap in Time Series Panels," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, pages 139-151.
    14. repec:kap:compec:v:50:y:2017:i:1:d:10.1007_s10614-016-9586-z is not listed on IDEAS
    15. Palm, Franz C. & Smeekes, Stephan & Urbain, Jean-Pierre, 2010. "A Sieve Bootstrap Test For Cointegration In A Conditional Error Correction Model," Econometric Theory, Cambridge University Press, vol. 26(03), pages 647-681, June.
    16. Franco, G.C. & Reisen, V.A. & Alves, F.A., 2013. "Bootstrap tests for fractional integration and cointegration: A comparison study," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 87(C), pages 19-29.
    17. Andrea Silvestrini, 2010. "Testing fiscal sustainability in Poland: a Bayesian analysis of cointegration," Empirical Economics, Springer, vol. 39(1), pages 241-274, August.
    18. Phillips, Peter C.B., 2010. "Bootstrapping I(1) data," Journal of Econometrics, Elsevier, vol. 158(2), pages 280-284, October.
    19. Gutierrez, Luciano, 2011. "Looking for Rational Bubbles in Agricultural Commodity Markets," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 120377, European Association of Agricultural Economists.
    20. Su, Jen-Je & Cheung, Adrian (Wai-Kong) & Roca, Eduardo, 2014. "Does Purchasing Power Parity hold? New evidence from wild-bootstrapped nonlinear unit root tests in the presence of heteroskedasticity," Economic Modelling, Elsevier, vol. 36(C), pages 161-171.
    21. Sevan Gulesserian & Mohitosh Kejriwal, 2014. "On the power of bootstrap tests for stationarity: a Monte Carlo comparison," Empirical Economics, Springer, vol. 46(3), pages 973-998, May.
    22. Shelef, Amit, 2016. "A Gini-based unit root test," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 763-772.
    23. Nunzio Cappuccio & Diego Lubian, 2016. "Unit Root Tests: The Role of the Univariate Models Implied by Multivariate Time Series," Econometrics, MDPI, Open Access Journal, vol. 4(2), pages 1-11, April.

    More about this item

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: 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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