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Dynamical cross-correlation of multiple time series Ising model

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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.

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Acknowledgments

Numerical calculations in this work were carried out at the Yukawa Institute Computer Facility and the facilities of the Institute of Statistical Mathematics. Discussions during the YITP workshop YITP-W-15-15 on ``Econophysics 2015'' were useful to complete this work.

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  1. Hiroshima University of Economics, Hiroshima, Japan

    Tetsuya Takaishi

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  1. Tetsuya Takaishi
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Correspondence to Tetsuya Takaishi.

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Takaishi, T. Dynamical cross-correlation of multiple time series Ising model. Evolut Inst Econ Rev 13, 455–468 (2016). https://doi.org/10.1007/s40844-016-0051-4

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