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Agent based reasoning for the non-linear stochastic models of long-range memory

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  • Kononovicius, A.
  • Gontis, V.

Abstract

We extend Kirman’s model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman’s agent based model is compared to the non-linear stochastic models of long-range memory in financial markets. The agent based model providing matching macroscopic description serves as a microscopic reasoning of the earlier proposed stochastic model exhibiting power law statistics.

Suggested Citation

  • Kononovicius, A. & Gontis, V., 2012. "Agent based reasoning for the non-linear stochastic models of long-range memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1309-1314.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1309-1314
    DOI: 10.1016/j.physa.2011.08.061
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    References listed on IDEAS

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    1. Alan Kirman, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(1), pages 137-156.
    2. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    3. Reimann, St. & Gontis, V. & Alaburda, M., 2011. "Interplay between positive feedbacks in the generalized CEV process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(8), pages 1393-1401.
    4. Thomas Lux & Michele Marchesi, 1999. "Scaling and criticality in a stochastic multi-agent model of a financial market," Nature, Nature, vol. 397(6719), pages 498-500, February.
    5. Simone Alfarano & Thomas Lux & Friedrich Wagner, 2005. "Estimation of Agent-Based Models: The Case of an Asymmetric Herding Model," Computational Economics, Springer;Society for Computational Economics, vol. 26(1), pages 19-49, August.
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