Mixed State Analysis of multivariate Time Series

When dealing with multivariate time series an important question one may ask is whether the measured signals are independent or not. Any interrelation can, for example, provide information about the underlying physical mechanisms or may be used to exploit possible redundancy in order to reduce the number of measurement channels. In linear systems theory the standard tool for detecting dependencies between two time series {xn} and {yn} is the linear correlation coefficient r (or Pearson’s r)