IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v24y2003i6p647-662.html
   My bibliography  Save this article

Rank Based Dickey–Fuller Test Statistics

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9892.2003.00327.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9892.2003.00327.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
    2. Breitung, Jorg & Gourieroux, Christian, 1997. "Rank tests for unit roots," Journal of Econometrics, Elsevier, vol. 81(1), pages 7-27, November.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ibrahim Onour, "undated". "Financial Integration of North Africa Stock Markets," API-Working Paper Series 0908, Arab Planning Institute - Kuwait, Information Center.
    2. Ibrahim A. Onour, 2009. "Financial integration of GCC capital markets: evidence of non-linear cointegration," Afro-Asian Journal of Finance and Accounting, Inderscience Enterprises Ltd, vol. 1(3), pages 251-265.
    3. V. A. Reisen & C. Lévy-Leduc & M. Bourguignon & H. Boistard, 2017. "Robust Dickey–Fuller tests based on ranks for time series with additive outliers," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(1), pages 115-131, January.
    4. Aparicio, Felipe M., 2003. "On the record properties of integrated time series," DES - Working Papers. Statistics and Econometrics. WS ws036414, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Song, Tao & Zheng, Tingguo & Tong, Lianjun, 2008. "An empirical test of the environmental Kuznets curve in China: A panel cointegration approach," China Economic Review, Elsevier, vol. 19(3), pages 381-392, September.
    6. Makoto Maejima & Gennady Samorodnitsky, 1999. "Certain Probabilistic Aspects of Semistable Laws," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(3), pages 449-462, September.
    7. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
    8. Härdle, Wolfgang Karl & Burnecki, Krzysztof & Weron, Rafał, 2004. "Simulation of risk processes," Papers 2004,01, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    9. Foad Shokrollahi & Marcin Marcin Magdziarz, 2020. "Equity warrant pricing under subdiffusive fractional Brownian motion of the short rate," Papers 2007.12228, arXiv.org, revised Nov 2020.
    10. Furrer, Hansjorg & Michna, Zbigniew & Weron, Aleksander, 1997. "Stable Lévy motion approximation in collective risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 20(2), pages 97-114, September.
    11. Yoon, Gawon, 2005. "An introduction to I([infinity]) processes," Economic Modelling, Elsevier, vol. 22(3), pages 473-483, May.
    12. Gary Madden & Scott J. Savage, 1998. "Sources of Australian Labour Productivity Change 1950–1994," The Economic Record, The Economic Society of Australia, vol. 74(227), pages 362-372, December.
    13. Ortobelli, Sergio & Rachev, Svetlozar & Schwartz, Eduardo, 2000. "The Problem of Optimal Asset Allocation with Stable Distributed Returns," University of California at Los Angeles, Anderson Graduate School of Management qt3zd6q86c, Anderson Graduate School of Management, UCLA.
    14. Michna, Zbigniew, 2008. "Asymptotic behavior of the supremum tail probability for anomalous diffusions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 413-417.
    15. Menn, Christian & Rachev, Svetlozar T., 2005. "A GARCH option pricing model with [alpha]-stable innovations," European Journal of Operational Research, Elsevier, vol. 163(1), pages 201-209, May.
    16. Żaba, Mariusz & Garbaczewski, Piotr & Stephanovich, Vladimir, 2013. "Lévy flights in confining environments: Random paths and their statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3485-3496.
    17. Kim, Panki, 2006. "Weak convergence of censored and reflected stable processes," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1792-1814, December.
    18. Donald J. Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Cowles Foundation Discussion Papers 1518, Cowles Foundation for Research in Economics, Yale University.
    19. Xu, Yong & Feng, Jing & Li, JuanJuan & Zhang, Huiqing, 2013. "Stochastic bifurcation for a tumor–immune system with symmetric Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4739-4748.
    20. Nolan, John P., 1998. "Parameterizations and modes of stable distributions," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 187-195, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jtsera:v:24:y:2003:i:6:p:647-662. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.