金融时间序列的多重分形类型的确定

The Determination of the Type of Multifractality of the Financial Time Series

为了探索股票时间序列的无标度性,利用多重分形消除趋势涨落分析的方法(MF-DFA)来研究沃尔玛股票指数(WMT)日收盘价.结果表明沃尔玛股票指数日收盘价的变化具有多重分形的特性.然后,随机打乱时间序列的次序,用MF-DFA方法分析打乱序列的多重分形性质,得出沃尔玛股票指数的多重分形主要是由概率密度函数产生的,分布多重分形占主导地位.比较原始序列和打乱序列的多重分形性质,得出打乱序列的多重分形性弱于原始序列的多重分形性.

To detect the scale qualities of stock market time series, we apply Muhifractal Detrended Fluctuation Analysis（ MF - DFA） to the time series of daily closing prices of Wal - Mart （WMT） at the American Stock Exchange. The research results show the time series of daily closing prices of Wal - Mart has multifractal properties. Besides, comparing the muhifractal detrended fluctuation analysis results for original series to those for shuffled seties, we obtain the muhifractality of the closing prices of WMT is mainly due to a broad probability density function, and the multifractality of the shuffled series is weaker than the original one.