Nonlinear Interrelation of Chaotic Time Series with Wavelet Transform and Recurrence Plot Analyses

Two relatively advanced and powerful analysis methods, i.e. coherence-wavelet transform and cross-recurrence plot, which are used to probe the nonlinear interrelation between different time series, have been applied to non-stationary time series in this paper. The case study uses the chaotic time series of astronomical observational data for the time interval from January 1966 to December 2010. We examined the phase dynamical properties between two data sets and found that the availability of a physically meaningful phase definition depends crucially on the appropriate choice of the reference frequencies. Furthermore, their phase shift is not only time-dependent but also frequency-dependent. We conclude that advanced nonlinear analysis approaches are more powerful than traditional linear methods when they are applied to analyze nonlinear and non-stationary dynamical behavior of complex physical systems.