Phase statistics approach to time series analysis

In this paper, an approach we introduced recently to study physiological and financial time series [Phys. Rev. E 73, 051917 (2006); Phys. Rev. E 73, 016118 (2006)] is reviewed. The approach . mainly consists of an application of the Hilbert-Huang method to decompose an empirical time series into a number of intrinsic mode functions (IMFs), calculation of the instantaneous phase of the resultant IMFs, and the statistics of the instantaneous phase for each IMF. To illustrate the approach, we consider cardiorespiratory synchronization and the phase distribution and phase correlation of financial time series as examples. The formulation of the approach is systematic and can be applied to the analysis of other time series.