Ising动力系统模拟收益率的多重分形分析

Simulation and multifractal analysis by stochastic Ising dynamic systems for returns

应用Ising模型和平均场理论构造符合股市收益率的动力系统,借助于计算机软件Mat-lab,利用蒙特卡洛模拟方法,通过调整参数模拟得出动力系统的收益率序列.分析发现:Ising动力系统构造的收益率同证券市场股票指数波动率一样具有厚尾等统计特征.对模拟收益率原序列和混洗后的序列进行多重分形分析,得出了模拟收益率序列存在分布多重分形和相关性多重分形的结论.

We considered a logarithmic returns process based on Ising model and mean field approximation.By adjusting parameters,we get the simulated returns of the dynamic systems by using mathematical soft Matlab and Monte Carlo simulatiomarket have similar statistical properties,such as fat-tail behavior.By comparing the multifractal detrended fluctuation analysis（MFDFA） results for original series with those for shuffled series,we can make a conclusion that multifractality of the returns both due to a broad probability density function and long-range correlations.