Diffusion entropy analysis on the scaling behavior of financial markets

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.