IDEAS home Printed from https://ideas.repec.org/a/bpj/sndecm/v4y2000i1nal2.html
   My bibliography  Save this article

A Generalized Fast Algorithm for BDS-Type Statistics

Author

Listed:
  • Mayer-Foulkes David

    (Centro de Investigación y Docencia Económicas)

Abstract

We provide a fast algorithm to calculate the m-dimensional distance histogram on which Brock, Dechert, and Sheinkman's (1987) BDS-type statistics are based. The algorithm generalizes a fast algorithm due to LeBaron by calculating the histogram for any finite set of distances simultaneously, and also using induction in m. By reordering the calculation appropriately, the algorithm also requires less memory and time. The two algorithms are compared using LeBaron's MS-DOS implementation in C and our Delphi (Windows Pascal) program. The generalized algorithm is faster when more than a few values of m and M (the distance parameter) are required, and is set up to calculate up to 255 values using short-integer arithmetic.

Suggested Citation

  • Mayer-Foulkes David, 2000. "A Generalized Fast Algorithm for BDS-Type Statistics," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 4(1), pages 1-7, April.
    • Handle: RePEc:bpj:sndecm:v:4:y:2000:i:1:n:al2
    DOI: 10.2202/1558-3708.1055
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/1558-3708.1055
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.2202/1558-3708.1055?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Brock, W. A., 1986. "Distinguishing random and deterministic systems: Abridged version," Journal of Economic Theory, Elsevier, vol. 40(1), pages 168-195, October.
    2. LeBaron Blake, 1997. "A Fast Algorithm for the BDS Statistic," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 2(2), pages 1-9, July.
    3. Mayer-Foulkes, David, 1995. "A statistical correlation dimension," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 277-293, September.
    Full references (including those not matched with items on IDEAS)

    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. Chaudhry, Muhammad Imran & Miranda, Mario J., 2018. "Complex price dynamics in vertically linked cobweb markets," Economic Modelling, Elsevier, vol. 72(C), pages 363-378.
    2. McKenzie, Michael D., 2001. "Chaotic behavior in national stock market indices: New evidence from the close returns test," Global Finance Journal, Elsevier, vol. 12(1), pages 35-53.
    3. Park, Joon Y. & Whang, Yoon-Jae, 2012. "Random walk or chaos: A formal test on the Lyapunov exponent," Journal of Econometrics, Elsevier, vol. 169(1), pages 61-74.
    4. Whang, Yoon-Jae & Linton, Oliver, 1999. "The asymptotic distribution of nonparametric estimates of the Lyapunov exponent for stochastic time series," Journal of Econometrics, Elsevier, vol. 91(1), pages 1-42, July.
    5. Scott C. Linn & Nicholas S. P. Tay, 2007. "Complexity and the Character of Stock Returns: Empirical Evidence and a Model of Asset Prices Based on Complex Investor Learning," Management Science, INFORMS, vol. 53(7), pages 1165-1180, July.
    6. Takala, Kari & Virén, Matti, 1995. "Testing nonlinear dynamics, long memory and chaotic behaviour with macroeconomic data," Research Discussion Papers 9/1995, Bank of Finland.
    7. Takala, Kari & Virén, Matti, 1993. "Testing nonlinearities with Finnish historical time series," Bank of Finland Research Discussion Papers 15/1993, Bank of Finland.
    8. Bonache, Adrien, 2008. "Les ventes de produits innovants à la mode sont-elles chaotiques? Le cas des ventes de Game Boy au Japon [Are innovative and fashion goods sales chaotic? The case of Game Boy sales in Japan]," MPRA Paper 12964, University Library of Munich, Germany.
    9. repec:zbw:bofrdp:1995_009 is not listed on IDEAS
    10. Marisa Faggini, 2011. "Chaotic Time Series Analysis in Economics: Balance and Perspectives," Working papers 25, Former Department of Economics and Public Finance "G. Prato", University of Torino.
    11. Panas, E., 2001. "Long memory and chaotic models of prices on the London Metal Exchange," Resources Policy, Elsevier, vol. 27(4), pages 235-246, December.
    12. Akhmet, Marat & Akhmetova, Zhanar & Fen, Mehmet Onur, 2014. "Chaos in economic models with exogenous shocks," Journal of Economic Behavior & Organization, Elsevier, vol. 106(C), pages 95-108.
    13. Brock, W.A. & Hommes, C.H., 1997. "Models of Compelxity in Economics and Finance," Working papers 9706, Wisconsin Madison - Social Systems.
    14. Czamanski, Daniel & Dormaar, Paul & Hinich, Melvin J. & Serletis, Apostolos, 2007. "Episodic nonlinearity and nonstationarity in Alberta's power and natural gas markets," Energy Economics, Elsevier, vol. 29(1), pages 94-104, January.
    15. Ayan Bhattacharya & Rudra Sensarma, 2013. "Non-linearities in Emerging Financial Markets: Evidence from India," IIM Kozhikode Society & Management Review, , vol. 2(2), pages 165-175, July.
    16. Michele Boldrin, 1988. "Paths of Optimal Accumulation in Two-Sector Models," UCLA Economics Working Papers 464, UCLA Department of Economics.
    17. Kevin J. Dooley & Andrew H. Van de Ven, 1999. "Explaining Complex Organizational Dynamics," Organization Science, INFORMS, vol. 10(3), pages 358-372, June.
    18. Bunyamin Demir & Nesrin Alptekin & Yilmaz Kilicaslan & Mehmet Ergen & Nilgun Caglairmak Uslu, 2015. "Forecasting Agricultural Production: A Chaotic Dynamic Approach," World Journal of Applied Economics, WERI-World Economic Research Institute, vol. 1(1), pages 65-80, June.
    19. Degiannakis, Stavros & Xekalaki, Evdokia, 2007. "Assessing the Performance of a Prediction Error Criterion Model Selection Algorithm in the Context of ARCH Models," MPRA Paper 96324, University Library of Munich, Germany.
    20. Christian Haxholdt & Erik R. Larsen & Ann van Ackere, 2003. "Mode Locking and Chaos in a Deterministic Queueing Model with Feedback," Management Science, INFORMS, vol. 49(6), pages 816-830, June.
    21. Matilla-Garcia, Mariano, 2007. "A non-parametric test for independence based on symbolic dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 31(12), pages 3889-3903, December.

    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:bpj:sndecm:v:4:y:2000:i:1:n:al2. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.