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Multivariate Markov chain modeling for stock markets

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  • Maskawa, Jun-ichi

Abstract

We study a multivariate Markov chain model as a stochastic model of the price changes of portfolios in the framework of the mean field approximation. The time series of price changes are coded into the sequences of up and down spins according to their signs. We start with the discussion for small portfolios consisting of two stock issues. The generalization of our model to arbitrary size of portfolio is constructed by a recurrence relation. The resultant form of the joint probability of the stationary state coincides with Gibbs measure assigned to each configuration of spin glass model. Through the analysis of actual portfolios, it has been shown that the synchronization of the direction of the price changes is well described by the model.

Suggested Citation

  • Maskawa, Jun-ichi, 2003. "Multivariate Markov chain modeling for stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 317-322.
    • Handle: RePEc:eee:phsmap:v:324:y:2003:i:1:p:317-322
    DOI: 10.1016/S0378-4371(02)01868-X
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    Citations

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    Cited by:

    1. João Nicolau & Flavio Riedlinger, 2015. "Estimation and inference in multivariate Markov chains," Statistical Papers, Springer, vol. 56(4), pages 1163-1173, November.
    2. Damásio, Bruno & Nicolau, João, 2024. "Time inhomogeneous multivariate Markov chains: Detecting and testing multiple structural breaks occurring at unknown dates," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    3. Riccardo De Blasis, 2020. "The price leadership share: a new measure of price discovery in financial markets," Annals of Finance, Springer, vol. 16(3), pages 381-405, September.
    4. Dibeh, Ghassan, 2007. "Contagion effects in a chartist–fundamentalist model with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 52-57.
    5. Bruno Damásio & João Nicolau, 2020. "Time Inhomogeneous Multivariate Markov Chains: Detecting and Testing Multiple Structural Breaks Occurring at Unknown," Working Papers REM 2020/0136, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    6. Wang, Luxuan & Niu, Ben & Wei, Junjie, 2016. "Dynamical analysis for a model of asset prices with two delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 297-313.

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