Advanced Search
MyIDEAS: Login

Cycles, determinism and persistence in agent-based games and financial time-series: part I

Contents:

Author Info

  • J. B. Satinover
  • D. Sornette
Registered author(s):

    Abstract

    The Minority Game (MG), the Majority Game (MAJG) and the Dollar Game ($G) are important and closely related versions of market-entry games designed to model different features of real-world financial markets. In a variant of these games, agents measure the performance of their available strategies over a fixed-length rolling window of prior time-steps. These are the Time Horizon MG/MAJG/$Gs (THMG, THMAJG, TH$G). Their probabilistic dynamics may be completely characterized in Markov-chain formulation. Games of both the standard and TH variants generate time-series that may be understood as arising from a stochastically perturbed determinism because a coin toss is used to break ties. The average over the binomially distributed coin tosses yields the underlying determinism. In order to quantify the degree of this determinism and of higher-order perturbations, we decompose the sign of the time-series they generate (analogous to a market price time-series) into a superposition of weighted Hamiltonian cycles on graphs—exactly in the TH variants and approximately in the standard versions. The cycle decomposition also provides a ‘dissection’ of the internal dynamics of the games and a quantitative measure of the degree of determinism. We discuss how the outperformance of strategies relative to agents in the THMG—the ‘illusion of control’—and the reverse in the THMAJG and TH$G, i.e. genuine control, may be understood on a cycle-by-cycle basis. The decomposition offers a new metric for comparing different game dynamics with real-world financial time-series and a method for generating predictors. We apply the cycle predictor to a real-world market, with significantly positive returns for the latter. Part I provides an overview of the paper and its methodologies with an appendix for the mathematical details of the Markov analysis of the THMG, THMAJG and TH$G. Part I also describes the cycle predictor and applies it to real-world financial series. Part II performs further analyses of the cycle decomposition method as applied to the time-series generated by agent-based models to gain insight into the ‘illusion of control’ that certain of these games demonstrate, i.e. the fact that the strategies outperform the agents that deploy them. Part II also illustrates both numerical and analytic methods for extracting cycles from a given time-series and applies the method to a number of different real-world data sets, in conjunction with an analysis of persistence.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://hdl.handle.net/10.1080/14697688.2012.670260
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 12 (2012)
    Issue (Month): 7 (February)
    Pages: 1051-1064

    as in new window
    Handle: RePEc:taf:quantf:v:12:y:2012:i:7:p:1051-1064

    Contact details of provider:
    Web page: http://www.tandfonline.com/RQUF20

    Order Information:
    Web: http://www.tandfonline.com/pricing/journal/RQUF20

    Related research

    Keywords:

    References

    No references listed on IDEAS
    You can help add them by filling out this form.

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:taf:quantf:v:12:y:2012:i:7:p:1051-1064. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Michael McNulty).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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