Graphic analysis and multifractal on percolation-based return interval series

Abstract

A financial time series model is developed and investigated by the oriented percolation system (one of the statistical physics systems). The nonlinear and statistical behaviors of the return interval time series are studied for the proposed model and the real stock market by applying visibility graph (VG) and multifractal detrended fluctuation analysis (MF-DFA). We investigate the fluctuation behaviors of return intervals of the model for different parameter settings, and also comparatively study these fluctuation patterns with those of the real financial data for different threshold values. The empirical research of this work exhibits the multifractal features for the corresponding financial time series. Further, the VGs deviated from both of the simulated data and the real data show the behaviors of small-world, hierarchy, high clustering and power-law tail for the degree distributions.