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A minimal noise trader model with realistic time series properties

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  • Alfarano, Simone
  • Lux, Thomas

Abstract

Simulations of agent-based models have shown that the stylized facts (unit-root, fat tails and volatility clustering) of financial markets have a possible explanation in the interactions among agents. However, the complexity, originating from the presence of non-linearity and interactions, often limits the analytical approach to the dynamics of these models. In this paper we show that even a very simple model of a financial market with heterogeneous interacting agents is capable of reproducing realistic statistical properties of returns, in close quantitative accordance with the empirical analysis. The simplicity of the system also permits some analytical insights using concepts from statistical mechanics and physics. In our model, the traders are divided into two groups : fundamentalists and chartists, and their interactions are based on a variant of the herding mechanism introduced by Kirman [22]. The statistical analysis of our simulated data shows long-term dependence in the auto-correlations of squared and absolute returns and hyperbolic decay in the tail of the distribution of the raw returns, both with estimated decay parameters in the same range like empirical data. Theoretical analysis, however, excludes the possibility of ’true’ scaling behavior because of the Markovian nature of the underlying process and the finite set of possible realized returns. The model, therefore, only mimics power law behavior. Similarly as with the phenomenological volatility models analyzed in LeBaron [25], the usual statistical tests are not able to distinguish between true or pseudo-scaling laws in the dynamics of our artificial market.

Suggested Citation

  • Alfarano, Simone & Lux, Thomas, 2006. "A minimal noise trader model with realistic time series properties," Economics Working Papers 2006-11, Christian-Albrechts-University of Kiel, Department of Economics.
  • Handle: RePEc:zbw:cauewp:5158
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    References listed on IDEAS

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    Cited by:

    1. David Morton de Lachapelle & Damien Challet, 2009. "Turnover, account value and diversification of real traders: evidence of collective portfolio optimizing behavior," Papers 0912.4723, arXiv.org, revised Jun 2010.
    2. repec:hal:journl:halshs-00185369 is not listed on IDEAS
    3. 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.
    4. Heni Boubaker & Nadia Sghaier, 2014. "Wavelet based Estimation of Time- Varying Long Memory Model with Nonlinear Fractional Integration Parameter," Working Papers 2014-284, Department of Research, Ipag Business School.
    5. Lux, Thomas, 2006. "Financial power laws: Empirical evidence, models, and mechanism," Economics Working Papers 2006-12, Christian-Albrechts-University of Kiel, Department of Economics.

    More about this item

    Keywords

    Speculative Dynamics; Fat Tails; Volatility Clustering; Herd Behavior;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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