配分函数法的改进及应用

针对传统配分函数难以处理分割子区间长度s不为时间序列长度T的约数或者T为质数的情况，采用类似多重分形去趋势波动法（MFDFA）的操作方式，提出修正配分函数法. 用二项式多重分形做数值模拟，得出的数值解与理论值几乎重合，表明修正配分函数法是有效的. 并较为详细地给出了配分函数法各参数的经济含义. 用修正配分函数法分析了上证A股指数的多重分形性，通过打乱序列、去极值、迭代振幅匹配傅里叶变换（IAAFT）研究了多重分形产生的原因. 结果表明：上证A股的分布、极值、序列的时变相关性均影响多重分形的形成，其中序列自相关性为主要因素.

The modified partition function method and its application

On account of traditional partition function hardly applying to the condition that the time series length T is a prime number or cannot be divisible by scaling s, we put forward a modified partition function whose algorithm procedure is similar to MFDFA. Using the numerical simulation of binomial multifractality, the result shows that the new method dealing with the multifractality of time series whose length is prime number is feasible and effective. The economic meaning of parameters in partition function are also discussed. By applying modified partition function, we investigate the multifractality of Shanghai A-share index. Through shuffling, removing extreme values and iterating amplitude adjusted fourier transform technological, we find that the temporal correlation, fat-tail distribution and extreme events are all contributed to the multifractality, but the autocorrelation in sequence plays an important role in the source of multifractality.