Complex system analysis of market return percolation model on Sierpinski carpet lattice fractal

This paper investigates the statistical behaviors of fluctuations of price changes in a stock market. The Sierpinski carpet lattice fractal and the percolation system are applied to develop a new random stock price for the financial market. The Sierpinski carpet is an infinitely ramified fractal and the percolation theory is usually used to describe the behavior of connected clusters in a random graph. The authors investigate and analyze the statistical behaviors of returns of the price model by some analysis methods, including multifractal analysis, autocorrelation analysis, scaled return interval analysis. Moreover, the authors consider the daily returns of Shanghai Stock Exchange Composite Index, and the comparisons of return behaviors between the actual data and the simulation data are exhibited.