(J. Timmer, Freiburg)
 

The analysis of multivariate time series has two roots. While in mathematics linear stochastic systems were the starting point, in physics nonlinear deterministic systems were the origin. The different types of dynamics considered led to different notions, e.g. coherence and phase spectra for linear stochastic systems and synchronisation for nonlinear deterministic systems. Accordingly, different mathematical methods have been developed to analyse time series from the different fields. The properties of the methods have mainly be investigated for systems of the field in which they have been developed, thus, demonstrating their sensitivity. Since in most applications the nature of the underlying dynamics is not known in advance but its inference is rather the goal of the analysis, it is important to develop methods with a high specificity for a certain type of multivariate dynamics in order to be able to draw reliable conclusions.