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Market mill dependence pattern in the stock market: Modeling of predictability and asymmetry via multi-component conditional distribution

Author

Listed:
  • Leonidov, Andrei
  • Trainin, Vladimir
  • Zaitsev, Alexander
  • Zaitsev, Sergey

Abstract

Recent studies have revealed a number of striking dependence patterns in high frequency stock price dynamics characterizing probabilistic interrelation between two consequent price increments x (push) and y (response) as described by the bivariate probability distribution P(x,y) [A. Leonidov, V. Trainin, A. Zaitsev, On collective non-gaussian dependence patterns in high frequency financial data, ArXiv:physics/0506072, A. Leonidov, V. Trainin, A. Zaitsev, S. Zaitsev, Market mill dependence pattern in the stock market: asymmetry structure, nonlinear correlations and predictability, arXiv:physics/0601098, A. Leonidov, V. Trainin, A. Zaitsev, S. Zaitsev, Market mill dependence pattern in the stock market: distribution geometry, moments and gaussization, arXiv:physics/0603103, A. Leonidov, V. Trainin, A. Zaitsev, S. Zaitsev, Market mill dependence pattern in the stock market: distribution geometry. Individual portraits, arXiv:physics/0605138]. There are two properties, the market mill asymmetries of P(x,y) and predictability due to nonzero z-shaped mean conditional response, that are of special importance. Main goal of the present paper is to put together a model reproducing both the z-shaped mean conditional response and the market mill asymmetry of P(x,y) with respect to the axis y=0. We develop a probabilistic model based on a multi-component ansatz for conditional distribution P(y|x) with push-dependent weights and means describing the both properties. In this paper we also introduce a quantitative measure of the relative weight of the asymmetric component of P(x,y) and show that the model reproduces a pattern observed in the market data. A relationship between the market mill asymmetry and predictability is discussed. A possible connection of the model to agent-based description of market dynamics is outlined.

Suggested Citation

  • Leonidov, Andrei & Trainin, Vladimir & Zaitsev, Alexander & Zaitsev, Sergey, 2007. "Market mill dependence pattern in the stock market: Modeling of predictability and asymmetry via multi-component conditional distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 240-252.
    • Handle: RePEc:eee:phsmap:v:386:y:2007:i:1:p:240-252
    DOI: 10.1016/j.physa.2007.07.062
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    References listed on IDEAS

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    1. Damien Challet & Tobias Galla, 2005. "Price return autocorrelation and predictability in agent-based models of financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 5(6), pages 569-576.
    2. Nikolay Gospodinov, 2005. "Testing For Threshold Nonlinearity in Short-Term Interest Rates," Journal of Financial Econometrics, Oxford University Press, vol. 3(3), pages 344-371.
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    4. Mandelbrot, Benoit B, 1971. "When Can Price Be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models," The Review of Economics and Statistics, MIT Press, vol. 53(3), pages 225-236, August.
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    1. Zaitsev, Sergey & Zaitsev, Alexander & Leonidov, Andrei & Trainin, Vladimir, 2009. "Market mill dependence pattern in the stock market: Multiscale conditional dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4624-4634.

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