Phase Statistics Approach to Physiological and Financial Time Series

Dynamical systems can usually be recorded by successive recording processes, and the characteristic behaviors are caught in corresponding time series. In this article, we review the phase statistics approach introduced recently to study physiological and financial time series. The approach consists of an application of the Hilbert-Huang transform 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. We consider cardiorespiratory synchronization and phase distribution and phase correlation of stock time series as examples. The applications to other time series are also briefly discussed.