Directed Nonlinear Interdependence

function [parameters, data] = timeseriesNLI(X,Y,k,m)

This function calculates directed Nonlinear Interdependence M(X|Y) from two timeseries X and Y. Nonlinear Interdependence relies on state space reconstruction and Taken's theorem. It doesn't assume any strict functional relationship between dyniamics of the underlying system. Exhanging X and Y will give M(Y|X), as it is a directional measure.

For more details refer to Andrzejak et. al. (2003).

Inputs:

X: first time series in 1-D vector

Y: second time series in 1-D vector

k: Number of nearest neighbours considered while calculating mean squared Euclidean distance Rk

m: Embedding dimension

Outputs:

parameter.NLI_estimate: NLI estimate (between 0 to 1)

data.signal1: X

data.signal2: Y

Example usage

>> X1 = Vtcr1(15001:20000);
>> Y1 = Vtcr2(15001:20000);
>> [parameters,data] = timeseriesNLI(X1, Y1, 32, 1024);
>> M = parameters.NLI_estimate;
>> signal1 = data.signal1;
>> signal2 = data.signal2;
>> M
M =

     1

NOTE: Our work builds upon the code included in the following works and implementations, so please do consider citing them:

References:

[1] Andrzejak, R. G., Kraskov, A., Stögbauer, H., Mormann, F., & Kreuz, T. (2003). Bivariate surrogate techniques: necessity, strengths, and caveats. Physical review E, 68(6), 066202.