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Rank Based Dickey–Fuller Test Statistics

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  • Stergios B. Fotopoulos
  • Sung K. Ahn

Abstract

This article provides various comprehensive comparisons between Breitung–Gouriéroux and Granger–Hallman rank statistics for the unit root test. New analytical asymptotic properties for the Granger–Hallman rank statistic are demonstrated. The statistic is of a Dickey–Fuller type, where the observations are replaced with their rank counterparts. Weak convergence results are given for the nonstationary random walk process when the errors are assumed to have higher than two moments. Empirical percentiles of both Breitung–Gouriéroux and Granger–Hallman rank statistics are presented for different sample sizes. In addition, empirical powers and sizes for these rank statistics and for the Dickey–Fuller test statistic are shown for different distributions of the error terms.

Suggested Citation

  • Stergios B. Fotopoulos & Sung K. Ahn, 2003. "Rank Based Dickey–Fuller Test Statistics," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(6), pages 647-662, November.
    • Handle: RePEc:bla:jtsera:v:24:y:2003:i:6:p:647-662
    DOI: 10.1111/j.1467-9892.2003.00327.x
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    References listed on IDEAS

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    1. C. W. J. Granger & Jeff Hallman, 1991. "Nonlinear Transformations Of Integrated Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 12(3), pages 207-224, May.
    2. Breitung, Jorg & Gourieroux, Christian, 1997. "Rank tests for unit roots," Journal of Econometrics, Elsevier, vol. 81(1), pages 7-27, November.
    3. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook9401, December.
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    Cited by:

    1. Wen-Jie Liu & Yu-Ting Bai & Xue-Bo Jin & Ting-Li Su & Jian-Lei Kong, 2022. "Adaptive Broad Echo State Network for Nonstationary Time Series Forecasting," Mathematics, MDPI, vol. 10(17), pages 1-21, September.

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