国际汇率的多重分形消除趋势波动分析

Multifractal Detrended Fluctuation Analysis of International Exchange Rates

基于多重分形消除趋势波动分析方法,对国际上3种主要的国际汇率收益序列进行实证研究。通过对收益时间序列进行重排处理和相位随机化处理,并将处理后的收益序列多重分形强度与原始序列进行比较,发现国际汇率的多重分形特征是由两个因素共同作用的,其中收益序列的波动相关性起主导作用,是形成多重分形特征的主要原因,而收益序列的胖尾概率分布对多重分形特征的形成也起到一定的作用。

Using MF-DFA, an empirical research on three international exchange rate time series is presented. It is found that the financial time series shows pronounced muhifractal characteristics. Furthermore, the sources of muhifractality are analyzed. Through shuffling procedure and phase randomization procedure, the original time series and the transformed time series are compared. It is found that there are two different types of sources for multifractality in time series, namely, fat-tailed probability distributions and nonlinear temporal correlations. Most multifractality of the data is due to different long-range correlations for small and large fluctuations, but the fat-tailed probability distributions also contribute to the muhifractal behavior of the time series.