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The Performance of Lag Selection and Detrending Methods for HEGY Seasonal Unit Root Tests

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  • Tomás del Barrio Castro
  • Denise R. Osborn
  • A.M. Robert Taylor

Abstract

This paper analyzes two key issues for the empirical implementation of parametric seasonal unit root tests, namely generalized least squares (GLS) versus ordinary least squares (OLS) detrending and the selection of the lag augmentation polynomial. Through an extensive Monte Carlo analysis, the performance of a battery of lag selection techniques is analyzed, including a new extension of modified information criteria for the seasonal unit root context. All procedures are applied for both OLS and GLS detrending for a range of data generating processes, also including an examination of hybrid OLS-GLS detrending in conjunction with (seasonal) modified AIC lag selection. An application to quarterly U.S. industrial production indices illustrates the practical implications of choices made.
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  • Tomás del Barrio Castro & Denise R. Osborn & A.M. Robert Taylor, 2012. "The Performance of Lag Selection and Detrending Methods for HEGY Seasonal Unit Root Tests," The School of Economics Discussion Paper Series 1228, Economics, The University of Manchester.
  • Handle: RePEc:man:sespap:1228
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    File URL: http://hummedia.manchester.ac.uk/schools/soss/economics/discussionpapers/EDP-1228.pdf
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    1. Tomás del Barrio Castro & Denise R. Osborn, 2012. "Non‐parametric testing for seasonally and periodically integrated processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(3), pages 424-437, May.
    2. 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(02), pages 527-560, April.
    3. 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.
    4. Rodrigues, Paulo M. M. & Taylor, A. M. Robert, 2004. "Alternative estimators and unit root tests for seasonal autoregressive processes," Journal of Econometrics, Elsevier, vol. 120(1), pages 35-73, May.
    5. Taylor, A. M. Robert, 1997. "On the practical problems of computing seasonal unit root tests," International Journal of Forecasting, Elsevier, vol. 13(3), pages 307-318, September.
    6. 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.
    7. 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.
    8. Taylor, A. M. Robert, 2005. "Variance ratio tests of the seasonal unit root hypothesis," Journal of Econometrics, Elsevier, vol. 124(1), pages 33-54, January.
    9. 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.
    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. 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.
    12. Burridge, Peter & Wallis, Kenneth F, 1984. "Unobserved-Components Models for Seasonal Adjustment Filters," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 350-359, October.
    13. 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.
    14. 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.
    15. Ghysels, Eric & Lee, Hahn S. & Noh, Jaesum, 1994. "Testing for unit roots in seasonal time series : Some theoretical extensions and a Monte Carlo investigation," Journal of Econometrics, Elsevier, vol. 62(2), pages 415-442, June.
    16. Hall, Alastair R, 1994. "Testing for a Unit Root in Time Series with Pretest Data-Based Model Selection," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 461-470, October.
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    Citations

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    Cited by:

    1. Tomás del Barrio Castro & Paulo M. M. Rodrigues & A. M. Robert Taylor, 2015. "Semi-Parametric Seasonal Unit Root Tests," DEA Working Papers 72, Universitat de les Illes Balears, Departament d'Economía Aplicada.
    2. repec:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-016-0688-9 is not listed on IDEAS
    3. repec:spr:empeco:v:52:y:2017:i:4:d:10.1007_s00181-016-1102-8 is not listed on IDEAS
    4. del Barrio Castro, Tomás & Hecq, Alain, 2016. "Testing for deterministic seasonality in mixed-frequency VARs," Economics Letters, Elsevier, vol. 149(C), pages 20-24.
    5. Tomás Barrio Castro & Andrii Bodnar & Andreu Sansó, 2017. "Numerical distribution functions for seasonal unit root tests with OLS and GLS detrending," Computational Statistics, Springer, vol. 32(4), pages 1533-1568, December.
    6. Politis, Dimitris, 2016. "HEGY test under seasonal heterogeneity," University of California at San Diego, Economics Working Paper Series qt2q4054kf, Department of Economics, UC San Diego.

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