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Bivariate time series analysis

Analysis of pairs of time series.

Focus

The main focus of analysis in bivariate time series analysis is determining the mode of interaction or cooperation between two systems.  The main questions concerning oscillatory systems include:

  • Are the systems coupled ?
  • Are the systems synchronized ?
  • Are the systems coupled unidirectionally (drive-response relationship ?)

 

Detecting synchronization

Synchronization is a term denoting many different forms of cooperation which however have one thing in common: at least one degree of freedom of motion is lost between two systems if they are synchronized.  In some areas (such as Neuroscience) the term synchronization denotes any form of coupling.

Detecting dependence

Systems which are not synchronized may nonetheless be coupled.  The systems keep all their degrees of freedom of motion but are dependent on each other in their future evolution.

 

Detecting directionality

Special forms of coupling are unidirectional couplings.  Unidirectional couplings indicate a drive-response relationship between two systems. This is sometimes called a master-slave relationship. Detecting such relationships is important when trying to understand complex networks of subsystems.