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A new approach to unit root testing

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  • Herwartz, Helmut
  • Siedenburg, Florian
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    Abstract

    A novel simulation based approach to unit root testing is proposed in this paper. The test is constructed from the distinct orders in probability of the OLS parameter estimates obtained from a spurious and an unbalanced regression, respectively. While the parameter estimate from a regression of two integrated and uncorrelated time series is of order Op(1), the estimate is of order Op(T-1) if the dependent variable is stationary. The test statistic is constructed as an inter quantile range from the empirical distribution obtained from regressing the standardized data sufficiently often on controlled random walks. GLS detrending (Elliott et al, 1996) and spectral density variance estimators (Perron and Ng, 1998) are applied to account for deterministic terms and residual autocorrelation in the data. A Monte Carlo study confirms that the proposed test has favorable empirical size properties and is powerful in local-to-unity neighborhoods. Testing for PPP for a sample of G6 economies, the proposed test yields results in favor of PPP for half of the sample economies while benchmark tests obtain at most one rejection of the random walk null hypothesis. --

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    Bibliographic Info

    Paper provided by Christian-Albrechts-University of Kiel, Department of Economics in its series Economics Working Papers with number 2009,06.

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    Date of creation: 2009
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    Handle: RePEc:zbw:cauewp:200906

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    Keywords: Unit root tests; simulation based test; simulation study; GLS detrending;

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    1. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July.
    2. Perron, P. & Ng, S., 1996. "An Autoregressive Spectral Density Estimator at Frequency Zero for Nonstationarity Tests," Cahiers de recherche 9611, Universite de Montreal, Departement de sciences economiques.
    3. Perron, P. & Ng, S., 1994. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Cahiers de recherche 9427, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    4. Wagner, Martin, 2005. "On PPP, Unit Roots and Panels," Economics Series 176, Institute for Advanced Studies.
    5. Alan M. Taylor & Mark Taylor, 2004. "The Purchasing Power Parity Debate," Working Papers 46, University of California, Davis, Department of Economics.
    6. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
    7. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    8. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
    9. Felipe Aparicio & Alvaro Escribano & Ana E. Sipols, 2006. "Range Unit-Root (RUR) Tests: Robust against Nonlinearities, Error Distributions, Structural Breaks and Outliers," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(4), pages 545-576, 07.
    10. 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.
    11. Breitung, Jörg & Gouriéroux, Christian, 1996. "Rank tests for unit roots," SFB 373 Discussion Papers 1996,9, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    12. Cheung, Yin-Wong & Lai, Kon S, 1995. "Lag Order and Critical Values of the Augmented Dickey-Fuller Test," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 277-80, July.
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