Transinformation of two time series.
The transinformation of two signals is one of the advanced coupling
measures. Unlike the cross correlation, it takes nonlinear dependencies into
account as well. "Transinformation" yields the information about a random variable
being stochastically dependent on a second variable. Derived from Shannon's
information theory, it is defined by
where denote the phase space densities of the observed
If the variables are stochastically independent, the transinformation I
vanishes. In case of dependencies (even if nonlinear), I has a positive
value. Furthermore, you can determine the temporal dependence of the coupling
by varying the relative shift .
Parameters of "Transinformation" are
- delay tau (no. of samples) for phase space reconstruction,
- embedding dimension m,
- relative shift delta of the second signal (as no. of samples),
- minimum relative radius rmin,
- maximum relative radius rmax,
- number n of radius steps
The output signal shows the transinformation as a function of the relative
radius for the phase space search. A plateau in the output graph indicates
the so-called scaling region, i.e. the range of radii where the phase space
reconstruction is best.
Note that since this function operates on 'pure' time series, scales and shifts of the given signals do not affect the result.
For a time-resolving computation of the transinformation use
y = Transinfo([x1,x2],tau,m,delta,rmin,rmax,n);
Pointwise transinformation, Conditional coupling divergence (PCCD),
Delta test, Mutual cross information,
Post event scan, Synchronicity histogram.