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Numerical Distribution Functions for Seasonal Unit Root Tests with OLS and GLS Detrending

Author

Listed:
  • Tomás del Barrio Castro

    (Universitat de les Illes Balears)

  • Andrii Bodnar

    (Universitat de les Illes Balears)

  • Andreu Sansó Rosselló

    (Universitat de les Illes Balears)

Abstract

This paper implements the approach introduced by MacKinnon (1994, 1996) to estimate the response surface of the test statistics of seasonal unit root tests with OLS and GLS detrending for quarterly and monthly time series. The Gauss code that is available in the supplementary material of the paper produces p-values for five test statistics depending on the sample size, deterministic terms and frequency of the data. A comparison with previous studies is undertaken, and an empirical example using airport passenger arrivals to a tourist destination is carried out. Quantile function coefficients are reported for simple computation of critical values for tests at 1%, 5% and 10% significance levels.

Suggested Citation

  • Tomás del Barrio Castro & Andrii Bodnar & Andreu Sansó Rosselló, 2015. "Numerical Distribution Functions for Seasonal Unit Root Tests with OLS and GLS Detrending," DEA Working Papers 73, Universitat de les Illes Balears, Departament d'Economía Aplicada.
    • Handle: RePEc:ubi:deawps:73
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    File URL: http://www.uib.es/depart/deaweb/deawp/pdf/w73.pdf
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    References listed on IDEAS

    as
    1. Smith, Richard J. & Taylor, A.M. Robert & del Barrio Castro, Tomas, 2009. "Regression-Based Seasonal Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 25(2), pages 527-560, April.
    2. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
    3. Burridge, Peter & Taylor, A M Robert, 2001. "On the Properties of Regression-Based Tests for Seasonal Unit Roots in the Presence of Higher-Order Serial Correlation," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 374-379, July.
    4. Harvey, David I. & van Dijk, Dick, 2006. "Sample size, lag order and critical values of seasonal unit root tests," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2734-2751, June.
    5. Joseph Beaulieu, J. & Miron, Jeffrey A., 1993. "Seasonal unit roots in aggregate U.S. data," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 305-328.
    6. Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2007. "Efficient tests of the seasonal unit root hypothesis," Journal of Econometrics, Elsevier, vol. 141(2), pages 548-573, December.
    7. Castro, Tomás del Barrio & Osborn, Denise R. & Taylor, A.M. Robert, 2012. "On Augmented Hegy Tests For Seasonal Unit Roots," Econometric Theory, Cambridge University Press, vol. 28(5), pages 1121-1143, October.
    8. 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.
    9. Diaz-Emparanza, Ignacio, 2014. "Numerical distribution functions for seasonal unit root tests," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 237-247.
    10. Gregoir, Stephane, 2006. "Efficient tests for the presence of a pair of complex conjugate unit roots in real time series," Journal of Econometrics, Elsevier, vol. 130(1), pages 45-100, January.
    11. Cragg, John G, 1983. "More Efficient Estimation in the Presence of Heteroscedasticity of Unknown Form," Econometrica, Econometric Society, vol. 51(3), pages 751-763, May.
    12. A. M. Robert Taylor, 1998. "Testing for Unit Roots in Monthly Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(3), pages 349-368, May.
    13. Burridge, Peter & Taylor, A. M. Robert, 2001. "On regression-based tests for seasonal unit roots in the presence of periodic heteroscedasticity," Journal of Econometrics, Elsevier, vol. 104(1), pages 91-117, August.
    14. Tomás Del Barrio Castro & Denise R. Osborn, 2011. "HEGY Tests in the Presence of Moving Averages," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 73(5), pages 691-704, October.
    15. Tom�s del Barrio Castro & Denise R. Osborn & A.M. Robert Taylor, 2016. "The Performance of Lag Selection and Detrending Methods for HEGY Seasonal Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 35(1), pages 122-168, January.
    16. Smith, Richard J. & Taylor, A. M. Robert, 1998. "Additional critical values and asymptotic representations for seasonal unit root tests," Journal of Econometrics, Elsevier, vol. 85(2), pages 269-288, August.
    17. Philip Hans Franses & Bart Hobijn, 1997. "Critical values for unit root tests in seasonal time series," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(1), pages 25-48.
    18. Richard J. Smith & A. M. Robert Taylor, 1999. "Likelihood Ratio Tests for Seasonal Unit Roots," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(4), pages 453-476, July.
    19. MacKinnon, James G, 1996. "Numerical Distribution Functions for Unit Root and Cointegration Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 601-618, Nov.-Dec..
    20. MacKinnon, James G, 1994. "Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 167-176, April.
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    Cited by:

    1. Tomás del Barrio Castro & Gianluca Cubadda & Denise R. Osborn, 2022. "On cointegration for processes integrated at different frequencies," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 412-435, May.
    2. Pradeep, Siddhartha, 2022. "Impact of diesel price reforms on asymmetricity of oil price pass-through to inflation: Indian perspective," The Journal of Economic Asymmetries, Elsevier, vol. 26(C).

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    More about this item

    Keywords

    HEGY test; GLS detrending; response surfaces;
    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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