In this paper the diffusion entropy technique is applied to investigate the scaling behavior of financial markets. The scaling behaviors of four representative stock markets, Dow Jones Industrial Average, Standard&Poor 500, Heng Seng Index, and Shang Hai Stock Synthetic Index, are almost the same; with the scale-invariance exponents all in the interval $[0.92, 0.95]$. These results provide a strong evidence of the existence of long-rang correlation in financial time series, thus several variance-based methods are restricted for detecting the scale-invariance properties of financial markets. In addition, a parsimonious percolation model for stock markets is proposed, of which the scaling behavior agrees with the real-life markets well.
Categories: physics.soc-ph