Abstract
We investigate cross-correlations between typical Japanese stocks collected through Yahoo!Japan website (http://finance.yahoo.co.jp/). By making use of multi-dimensional scaling (MDS) for the cross-correlation matrices, we draw two-dimensional scattered plots in which each point corresponds to each stock. To make a clustering for these data plots, we utilize the mixture of Gaussians to fit the data set to several Gaussian densities. By minimizing the so-called Akaike Information Criterion (AIC) with respect to parameters in the mixture, we attempt to specify the best possible mixture of Gaussians. It might be naturally assumed that all the two-dimensional data points of stocks shrink into a single small region when some economic crisis takes place. The justification of this assumption is numerically checked for the empirical Japanese stock data, for instance, those around 11 March 2011.
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Acknowledgements
We thank Frederic Abergel, Anirban Chakraborti, Asim K. Ghosh and Bikas K. Chakrabarti, and all the other organizers of Econophysics-Kolkata VI. One of the authors (JI) thanks Enrico Scalas, Giacomo Livan for valuable discussion. This work was financially supported by Grant-in-Aid for Scientific Research (C) of Japan Society for the Promotion of Science, No. 22500195.
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Ibuki, T., Suzuki, S., Inoue, Ji. (2013). Cluster Analysis and Gaussian Mixture Estimation of Correlated Time-Series by Means of Multi-dimensional Scaling. In: Abergel, F., Chakrabarti, B., Chakraborti, A., Ghosh, A. (eds) Econophysics of Systemic Risk and Network Dynamics. New Economic Windows. Springer, Milano. https://doi.org/10.1007/978-88-470-2553-0_15
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DOI: https://doi.org/10.1007/978-88-470-2553-0_15
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