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A new approach to unit root testing

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  • Herwartz, Helmut
  • Siedenburg, Florian

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.

Suggested Citation

  • Herwartz, Helmut & Siedenburg, Florian, 2009. "A new approach to unit root testing," Economics Working Papers 2009-06, Christian-Albrechts-University of Kiel, Department of Economics.
  • Handle: RePEc:zbw:cauewp:200906
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    References listed on IDEAS

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    1. Pierre Perron & Serena Ng, 1996. "Useful Modifications to some Unit Root Tests with Dependent Errors and their Local Asymptotic Properties," Review of Economic Studies, Oxford University Press, vol. 63(3), pages 435-463.
    2. Martin Wagner, 2008. "On PPP, unit roots and panels," Empirical Economics, Springer, vol. 35(2), pages 229-249, September.
    3. Alan M. Taylor & Mark P. Taylor, 2004. "The Purchasing Power Parity Debate," Journal of Economic Perspectives, American Economic Association, vol. 18(4), pages 135-158, Fall.
    4. 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 277-280, July.
    5. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    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. Perron, Pierre & Ng, Serena, 1998. "An Autoregressive Spectral Density Estimator At Frequency Zero For Nonstationarity Tests," Econometric Theory, Cambridge University Press, vol. 14(05), pages 560-603, October.
    8. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    9. 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.
    10. Breitung, Jorg & Gourieroux, Christian, 1997. "Rank tests for unit roots," Journal of Econometrics, Elsevier, vol. 81(1), pages 7-27, November.
    11. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
    12. 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, July.
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    More about this item

    Keywords

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

    JEL classification:

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

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