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Dynamical cross-correlation of multiple time series Ising model

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  • Tetsuya Takaishi

    (Hiroshima University of Economics)

Abstract

Using an Ising-based model extended to simulate multiple stock time series, we perform a large-scale simulation for a financial system with 100 stocks. We find that the financial system shows fat-tailed return distributions and the system volatility level measured as an average of absolute-returns changes over time. We investigate the dynamical properties of cross-correlation matrices among stocks and find that the eigenvalue distributions of the cross-correlation matrices deviate from those of the random matrix theory. It is found that the cumulative risk fraction (CRF) constructed from the largest eigenvalues changes at periods where the volatility level is high. The inverse participation ratio (IPR) and its higher-power version, IPR6, also exhibit the changes at the same high volatility periods. Therefore, the CRF, IPR, and IPR6 are expected to be useful measurements to identify abnormal states such as high-volatility periods.

Suggested Citation

  • Tetsuya Takaishi, 2016. "Dynamical cross-correlation of multiple time series Ising model," Evolutionary and Institutional Economics Review, Springer, vol. 13(2), pages 455-468, December.
    • Handle: RePEc:spr:eaiere:v:13:y:2016:i:2:d:10.1007_s40844-016-0051-4
    DOI: 10.1007/s40844-016-0051-4
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    4. Bornholdt, Stefan, 2022. "A q-spin Potts model of markets: Gain–loss asymmetry in stock indices as an emergent phenomenon," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).

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    More about this item

    Keywords

    Ising model; Cross-correlation; Random matrix theory; Cumulative risk fraction; Inverse participation ratio;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G01 - Financial Economics - - General - - - Financial Crises
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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