Fluctuation entropy and complexity of financial percolation model with random jump on gasket fractal lattice

Abstract

In an attempt to investigate the statistical complexity mechanics of stock markets, a novel stochastic interacting financial dynamics is proposed by Sierpinski gasket fractal lattice percolation with random jump. Sierpinski gasket is a famous example of fractals, and Sierpinski gasket lattice is a fractal-like graph which corresponds to that. Fuzzy entropy and multiscale composite complexity synchronization are applied to investigate the complexity and synchronization behaviors of security time series. Further, the similar statistical methods are used to analyze the actual stock market for comparison, which verifies the rationality and effectiveness of the financial model. The results suggest that the randomness of return series from the model increases with the increase of the parameter, which indicates the frequency of unexpected events affecting the stock market within the unit time and shows that the time series basically become more synchronous as the time scale increases. The empirical studies indicate that this stochastic price model is reasonable to a certain degree.