Volatility clustering and long memory of financial time series and financial price model

We investigate the statistical behaviors of long-range dependence phenomena and volatility clustering of logarithmic returns for a financial price model and two real financial market indexes (Shanghai Composite Index and Hang Seng Index). The price process is modeled by interacting voter particle system, where the vote model is a continuous time Markov process, which originally represents a voterʼs attitude on a particular topic, that is, voters reconsider their opinions at times distributed according to independent exponential random variables. In this paper, GARCH(1,1) model and autocorrelation analysis are applied to demonstrate the volatility clustering properties for the actual return series and the simulative data by comparison, and modified R/S analysis and DFA method are employed to evaluate the corresponding long-range memory behaviors.