FLUCTUATION BEHAVIOR OF FINANCIAL RETURN INTERVAL SERIES MODEL FOR PERCOLATION ON SIERPINSKI CARPET LATTICE

A financial time series model is developed by the percolation system on the Sierpinski carpet lattice fractal. We investigate the fluctuation behaviors of various shuffled return interval series (original, randomly shuffled and by Zipf method) by applying the multifractal detrended fluctuation analysis for the financial model and Shanghai composite index. Numerically we show the fluctuations of the generalized Hurst exponents for different order parameters, the nonlinear dependence of these scaling exponents and the singularity spectrum show that the return intervals possess the multifractality. By comparing the MF-DFA empirical results of the original series to those for the randomly shuffled series, the empirical research exhibits the multifractality is mainly due to the contributions of long-range correlations as well as the broad probability density function. Further we show that the shuffled series by Zipf method exhibits the similar properties for the positive orders.