Dynamical Analysis of Stock Market Instability by Cross-correlation Matrix

5th International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Takaishi, Tetsuya^1

Hiroshima University of Economics, Hiroshima

731-0192, Japan^1

关键词: Cross correlation matrices;    Dynamical analysis;    Dynamical evolution;    Market instability;    Principal Components;    Principal components analysis;    Random matrix theory;    Tokyo Stock Exchange;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/738/1/012077/pdf
DOI  :  10.1088/1742-6596/738/1/012077

来源: IOP

【 摘 要 】

We study stock market instability by using cross-correlations constructed from the return time series of 366 stocks traded on the Tokyo Stock Exchange from January 5, 1998 to December 30, 2013. To investigate the dynamical evolution of the cross-correlations, crosscorrelation matrices are calculated with a rolling window of 400 days. To quantify the volatile market stages where the potential risk is high, we apply the principal components analysis and measure the cumulative risk fraction (CRF), which is the system variance associated with the first few principal components. From the CRF, we detected three volatile market stages corresponding to the bankruptcy of Lehman Brothers, the 2011 Tohoku Region Pacific Coast Earthquake, and the FRB QE3 reduction observation in the study period. We further apply the random matrix theory for the risk analysis and find that the first eigenvector is more equally de-localized when the market is volatile.