Coupling detrended fluctuation analysis for analyzing coupled nonstationary signals

L. Hedayatifar, M. Vahabi, G. R. Jafari
2011 Physical Review E  
When many variables are coupled to each other, a single case study could not give us thorough and precise information. When these time series are stationary, different methods of random matrix analysis and complex networks can be used. But, in nonstationary cases, the multifractal-detrended-cross-correlation-analysis (MF-DXA) method was introduced for just two coupled time series. In this article, we have extended the MF-DXA to the method of coupling detrended fluctuation analysis (CDFA) for
more » ... case when more than two series are correlated to each other. Here, we have calculated the multifractal properties of the coupled time series, and by comparing CDFA results of the original series with those of the shuffled and surrogate series, we can estimate the source of multifractality and the extent to which our series are coupled to each other. We illustrate the method by selected examples from air pollution and foreign exchange rates.
doi:10.1103/physreve.84.021138 pmid:21928980 fatcat:7b7i3r454jftpj5rcylhzu36ly