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Predictive asymmetry

# CausalityTools.CausalityTests.predictive_asymmetry — Function.

predictive_asymmetry(source, target, test::PredictiveAsymmetryTest{T, N}) where {T <: TransferEntropyCausalityTest, N}

Compute the predictive asymmetry from source to target using the provided predictive test p. The test can be a VisitationFrequencyTest, TransferOperatorGridTest or NearestNeighbourMITest and has to be defined for prediction lags symmetrically around zero.

Example

We'll use the nonlinear3d system, which consists of three variables and is unidirectionally coupled $x \to y \to z$.

# Example data
sys = nonlinear3d()
npts = 300
orbit = trajectory(sys, npts, Ttr = 300);
x, y, z = columns(orbit);

# Test setup
η_max = 10
ηs = [-η_max:-1; 1:η_max]
bin = RectangularBinning(floor(Int, npts^(1/4)))
test = VisitationFrequencyTest(ηs = ηs, binning = bin)
pa_test = PredictiveAsymmetryTest(test)

# Analysis
pas_xy = causality(x, y, pa_test)
pas_yx = causality(y, x, pa_test)
pas_yz = causality(y, z, pa_test)
pas_zy = causality(z, y, pa_test)

[pas_xy pas_yx pas_yz pas_zy]

If the test correctly picked up the correct directionality, then the values of of asymmetries corresponding to the causal interactions (1^st and 3^rd column) should be mostly positive, and those corresponding to non-causal interactions should be mostly negative.

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