## Transinformation

Purpose
Description
Tips
Macro Synopsis
Modules
Related Functions

### Purpose

Transinformation of two time series.

### Description

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 variables.
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.

### Tips

For a time-resolving computation of the transinformation use

### Macro Synopsis

y = Transinfo([x1,x2],tau,m,delta,rmin,rmax,n);
signal x1,x2,y;
int tau,m,delta;
float rmin,rmax;
int n;

Nonlinear

### Related Functions

Pointwise transinformation, Conditional coupling divergence (PCCD), Delta test, Mutual cross information, Post event scan, Synchronicity histogram.