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Spectral Approach to Parameter-Free Unit Root Testing

Author

Listed:
  • Natalia Bailey

    (Queen Mary University of London)

  • Liudas Giraitis

    (Queen Mary University of London)

Abstract

A relatively simple frequency-type testing procedure for unit root potentially contaminated by an additive stationary noise is introduced, which encompasses general settings and allows for linear trends. The proposed test for unit root versus stationarity is based on a finite number of periodograms computed at low Fourier frequencies. It is not sensitive to the selection of tuning parameters defining the range of frequencies so long as they are in the vicinity of zero. The test does not require augmentation, has parameter-free non-standard asymptotic distribution and is correctly sized. The consistency rate under the alternative of stationarity reveals the relation between the power of the test and the long-run variance of the process. The finite sample performance of the test is explored in a Monte Carlo simulation study, and its empirical application suggests rejection of the unit root hypothesis for some of the Nelson-Plosser time series.

Suggested Citation

  • Natalia Bailey & Liudas Giraitis, 2015. "Spectral Approach to Parameter-Free Unit Root Testing," Working Papers 746, Queen Mary University of London, School of Economics and Finance.
    • Handle: RePEc:qmw:qmwecw:746
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    References listed on IDEAS

    as
    1. Karim M. Abadir & Walter Distaso & Liudas Giraitis, 2011. "An I() model with trend and cycles," Post-Print hal-00834425, HAL.
    2. Cheung, Yin-Wong & Lai, Kon S, 1995. "Lag Order and Critical Values of a Modified Dickey-Fuller Test," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 57(3), pages 411-419, August.
    3. Choi, In & Phillips, Peter C. B., 1993. "Testing for a unit root by frequency domain regression," Journal of Econometrics, Elsevier, vol. 59(3), pages 263-286, October.
    4. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
    5. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    6. 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.
    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. Giraitis, Liudas & Leipus, Remigijus & Philippe, Anne, 2006. "A Test For Stationarity Versus Trends And Unit Roots For A Wide Class Of Dependent Errors," Econometric Theory, Cambridge University Press, vol. 22(6), pages 989-1029, December.
    9. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    10. Perron, Pierre, 1988. "Trends and random walks in macroeconomic time series : Further evidence from a new approach," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 297-332.
    11. DeJong, David N, et al, 1992. "Integration versus Trend Stationarity in Time Series," Econometrica, Econometric Society, vol. 60(2), pages 423-433, March.
    12. Lucas, Andre, 1995. "An outlier robust unit root test with an application to the extended Nelson-Plosser data," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 153-173.
    13. Fan, Yanqin & Gençay, Ramazan, 2010. "Unit Root Tests With Wavelets," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1305-1331, October.
    14. Phillips, Peter, 1999. "Discrete Fourier Transforms of Fractional Processes August," Working Papers 149, Department of Economics, The University of Auckland.
    15. Phillips, P C B, 1991. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 333-364, Oct.-Dec..
    16. 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.
    17. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    18. Shelef, Amit, 2016. "A Gini-based unit root test," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 763-772.
    19. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2011. "An I(d) model with trend and cycles," Journal of Econometrics, Elsevier, vol. 163(2), pages 186-199, August.
    20. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
    21. Westerlund, Joakim, 2014. "On the choice of test for a unit root when the errors are conditionally heteroskedastic," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 40-53.
    22. repec:hal:journl:peer-00834425 is not listed on IDEAS
    23. 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.
    24. Cochrane, John H., 1991. "A critique of the application of unit root tests," Journal of Economic Dynamics and Control, Elsevier, vol. 15(2), pages 275-284, April.
    25. Schotman, Peter C & van Dijk, Herman K, 1991. "On Bayesian Routes to Unit Roots," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 387-401, Oct.-Dec..
    26. 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.
    27. Lopez, J. Humberto, 1997. "The power of the ADF test," Economics Letters, Elsevier, vol. 57(1), pages 5-10, November.
    28. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    29. repec:bla:jecsur:v:12:y:1998:i:5:p:423-69 is not listed on IDEAS
    30. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
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    Cited by:

    1. Gennadi Gromykov & Mohamedou Ould Haye & Anne Philippe, 2018. "A frequency-domain test for long range dependence," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 513-526, October.

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    More about this item

    Keywords

    Unit root test; Additive noise; Parameter-free distribution;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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