Coupling detrended fluctuation analysis for analyzing coupled nonstationary signals.

Area of Science:

• Complex systems analysis
• Time series analysis
• Statistical physics

Background:

• Analyzing coupled variables requires methods beyond single case studies.
• Stationary time series can be analyzed using random matrix theory and complex networks.
• Nonstationary coupled time series analysis is limited, with multifractal-detrended-cross-correlation-analysis (MF-DXA) only applicable to pairs.

Purpose of the Study:

• To extend MF-DXA for analyzing multifractality in more than two correlated time series.
• To develop a method for quantifying the coupling strength and multifractality sources in complex systems.
• To provide a robust analytical tool for nonstationary multivariate time series.

Main Methods:

• Developed the coupling detrended fluctuation analysis (CDFA) method, an extension of MF-DXA.
• Calculated multifractal properties of coupled time series.
• Compared CDFA results of original series with shuffled and surrogate series to identify multifractality sources and coupling extent.

Main Results:

• The CDFA method successfully extends multifractal analysis to systems with more than two correlated time series.
• By comparing with surrogate data, the method can distinguish true multifractality and coupling from random correlations.
• Illustrative examples from air pollution and foreign exchange rates demonstrate the method's applicability.

Conclusions:

• CDFA provides a powerful new approach for analyzing complex, multifractal behaviors in multivariate, nonstationary time series.
• The method allows for a deeper understanding of the interconnectedness and underlying dynamics within complex systems.
• This technique has broad applications in fields dealing with multivariate time series data.