Multifractal Temporally Weighted Detrended Cross-correlation Analysis To Quantify Power-law Cross-correlation And Its Application To Stock Markets

A new method—multifractal temporally weighted detrended cross-correlation analysis (MF-TWXDFA) which is based on multifractal temporally weighted detrended fluctuation analysis (MF-TWDFA) and multifractal cross-correlation analysis (MFCCA) is proposed in this thesis. One innovation of the method is applying geographically weighted regression thought to estimate the trend in detrending step. The other lies in takeing into consideration of both the fluctua-tion information and the sign information in the corresponding detrended cross-covariance function. To test the performance of MF-TWXDFA algorithm, we apply it and 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 market,and find that power-law cross-correlation between stock returns is significantly multifractal. A new coefficient—MF-TWXDFA cross-correlation coefficient is al-so defined to quantify the levels of cross-correlation between two time series.