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Numerical distribution functions for seasonal unit root tests with OLS and GLS detrending

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Abstract

This paper implements the approach introduced by MacKinnon (J Bus Econ Stat 12:167–176, 1994, J Appl Econom 11:601–618, 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.

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Notes

  1. It took around 4 weeks of computing time and 250 GB of disk space to store the results. The simulations were performed on \(\hbox {Intel}^{\circledR }\, \hbox {Xeon}^{\circledR }\) CPU E5-2470.

  2. For the \(F_{k}\) tests (\(k=1,2\, {\ldots },\, 5\)) we have 6 480 observations in the monthly case. In fact, there are five F-type tests with the same asymptotic distribution, thus we used the test results of the entire simulation in order to increase the efficiency of estimates. The resulting numerical distribution is valid for testing each of the five \(H_{0,k}\) hypothesis.

  3. We are very grateful to an anonymous referee for this suggestion. The results from this simulation experiment are available upon request.

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Acknowledgments

We would like to thank an anonymous referee for his/her helpful comments. Tomas del Barrio Castro and Andreu Sansó knowledge financial support from Spanish Ministerio de Educación, Cultura y Deporte under Grant ECO2014-58991-C3-3-R.

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Authors and Affiliations

  1. Department of Applied Economics, University of the Balearic Islands, Palma de Mallorca, Spain

    Tomás del Barrio Castro, Andrii Bodnar & Andreu Sansó

Authors
  1. Tomás del Barrio Castro
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  2. Andrii Bodnar
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  3. Andreu Sansó
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Corresponding author

Correspondence to Tomás del Barrio Castro.

Appendix

Appendix

See Tables 3, 4, 5, 6, 7, 8 and 9.

Table 3 Quantile coefficients for monthly data, \(p=1\), 5 and 10 %, case of GLS-detrending
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Table 4 Quantile coefficients for quarterly data, \(p=1\), 5 and 10 %, case of GLS-detrending
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Table 5 Quantile coefficients for monthly data, \(p=1\), 5 and 10 %, OLS-detrending
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Table 6 Quantile coefficients for quarterly data, \(p=1\), 5 and 10 %, OLS detrending
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Table 7 Critical values obtained from the response surface with low \(\hbox {R}^{2}\) compared to previously published values
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Table 8 Critical values that differ from previous studies
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Table 9 Cross verification results
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del Barrio Castro, T., Bodnar, A. & Sansó, A. Numerical distribution functions for seasonal unit root tests with OLS and GLS detrending. Comput Stat 32, 1533–1568 (2017). https://doi.org/10.1007/s00180-016-0688-9

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  • DOI: https://doi.org/10.1007/s00180-016-0688-9

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