Wei Yun-Lan, Yu Zu-Guo, Zou Hai-Long, Anh Vo
Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education and Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan 411105, China.
School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane Q4001, Australia.
Chaos. 2017 Jun;27(6):063111. doi: 10.1063/1.4985637.
A new method-multifractal temporally weighted detrended cross-correlation analysis (MF-TWXDFA)-is proposed to investigate multifractal cross-correlations in this paper. This new method is based on multifractal temporally weighted detrended fluctuation analysis and multifractal cross-correlation analysis (MFCCA). An innovation of the method is applying geographically weighted regression to estimate local trends in the nonstationary time series. We also take into consideration the sign of the fluctuations in computing the corresponding detrended cross-covariance function. To test the performance of the MF-TWXDFA algorithm, we apply it and the MFCCA method on simulated and actual series. Numerical tests on artificially simulated series demonstrate that our method can accurately detect long-range cross-correlations for two simultaneously recorded series. To further show the utility of MF-TWXDFA, we apply it on time series from stock markets and find that power-law cross-correlation between stock returns is significantly multifractal. A new coefficient, MF-TWXDFA cross-correlation coefficient, is also defined to quantify the levels of cross-correlation between two time series.
本文提出了一种新方法——多重分形时间加权去趋势互相关分析（MF-TWXDFA），用于研究多重分形互相关。这种新方法基于多重分形时间加权去趋势波动分析和多重分形互相关分析（MFCCA）。该方法的一个创新点是应用地理加权回归来估计非平稳时间序列中的局部趋势。在计算相应的去趋势互协方差函数时，我们还考虑了波动的符号。为了测试MF-TWXDFA算法的性能，我们将其与MFCCA方法应用于模拟和实际序列。对人工模拟序列的数值测试表明，我们的方法可以准确检测两个同时记录序列的长程互相关。为了进一步展示MF-TWXDFA的实用性，我们将其应用于股票市场的时间序列，发现股票回报之间的幂律互相关具有显著的多重分形性。还定义了一个新的系数——MF-TWXDFA互相关系数，以量化两个时间序列之间的互相关水平。
