多重分形消除趋势波动分析法（MF-DFA）不仅能够去除股票时间序列的长期趋势波动，还能够精确反应股票时间序列的多重分形特性。首先利用MF-DFA方法对股票时间序列进行多重分形分析，结果表明，相比标准多重分析，MF-DFA方法更能反映时间序列的多重分形特性。其次，定义一种以多重分形谱参数作为相似性度量函数的聚类方法对股票时间序列进行聚类。最后，在Markowitz提出的“期望均值收益-收益方差”（M-V）模型的基础上，把聚类结果运用股票投资组合当中。采用上海证券市场28支股票进行实验验证表明，在给定的收益率下，采用基于多重分形谱参数的聚类方法的股票组合可以得到比随机组合更小的风险水平。%The method of multi-fractal detrended fluctuation analysis (MF-DFA) can not only be able to remove the fluctuations of the long-term trend in the stock market time series, but also be able to describe the multi-fractal characteristics. First of all, this paper uses the MF-DFA to analyze the multi-fractal characteristics of the stock market time series and the result shows that the method of MF-DFA is more efficient. Secondly, it defines a similarity measure function of clustering which use the parameters of multi-fractal spectrum as their parameters on the stock time series clustering. Finally, based on the Markowitz proposed the rule of expected mean and the variance of return (M-V rule), it applies the clustering results into the stock portfolio. According to the experiment result, a portfolio with more return and lower risk is reached.
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