Pointwise transinformation of two time series
The "Pointwise transinformation" is a time-resolving variant of the Transinformation,
returning an estimation of the transinformation for each sample
(point in time).
The defining formula for the i-th time step is :
where the transinformation I is a function of the relative shift
and relative phase space radius r, given for every sample
point i. denotes the probability to find a point of the
reconstructed trajectory within a sphere of radius r around the i-th
phase space point. and refer to the
phase spaces of the time series x1 and x2, respectively.
refers to the common phase space of the two systems.
Parameters of "Pointwise transinformation" are
- delay of coordinates tau (in no. of samples),
- embedding dimension m of the phase space reconstruction,
- relative shift delta of the 2nd signal (in no. of samples),
- relative radius r
Due to the dual logarithm in the formula above the output unit is 'bits'.
Note that since this function operates on 'pure' time series, scales and shifts of the given signals do not affect the result.
Using "Pointwise transinformation", you can detect changes in the coupling of two interacting
systems, indicated by an increase or decrease in the time course of the
y = PointTransinfo([x1,x2],tau,m,delta,r);
Conditional coupling divergence (PCCD), Delta test,
Mutual cross information, Post event scan,
Synchronicity histogram, Transinformation.