Multifractal Temporally Weighted Detrended Partial Cross-correlation Analysis Of Nonstationary Time Series

When common factors strongly influence two cross-correlated time series recorded in complex natural and social systems,the results will be biased if we use detrended cross-correlation analysis without considering these common fac-tors.A new method——multifractal temporally weighted detrended partial cross-correlation analysis(MF-TWDPCCA)which is based on multifractal temporal-ly weighted detrended cross-correlation analysis(MF-TWXDFA)and multifrac-tal partial cross-correlation analysis(MF-DPXA)is proposed in this thesis.The innovation of this algorithm is to introduce partial correlation analysis to deal with two time series which are affected by the common external forces.-We use MF-TWDPCCA to depict the intrinsic cross-correlations between the two simul-taneously recorded time series after removing the effects of other potential time series.Numerical simulation demonstrate that MF-TWDPCCA partial correlation coefficient is more advantageous than MF-DPXA.To further show the utility of MF-TWDPCCA,we use it to investigate multifractal time series,and find that MF-TWDPCCA method quantifies the hidden multifractal property while the MF-TWXDFA method fails.This shows that partial cross-correlation analysis is necessary when analyzing time series affected by common factors.