Experimental

Here we list implemented methods that do not yet appear in peer-reviewed journals, but are found, for example, in pre-print servers like arXiv.

The API for these methods, and their return values, may change at any time until they appear as part of the public API. Use them wisely.

Predictive asymmetry

CausalityTools.predictive_asymmetry — Function

predictive_asymmetry(estimator::TransferEntropyEstimator, ηs; s, t, [c],
    dTf = 1, dT = 1, dS = 1, τT = -1, τS = -1, [dC = 1, τC = -1],
    normalize::Bool = false, f::Real = 1.0, base = 2) → Vector{Float64}

Compute the predictive asymmetry (Haaga et al., 2020) 𝔸(s → t) for source time series s and target time series t over prediction lags ηs, using the given estimator and embedding parameters dTf, dT, dS, τT, τS (see also EmbeddingTE)

If a conditional time series c is provided, compute 𝔸(s → t | c). Then, dC and τC controls the embedding dimension and embedding lag for the conditional variable.

Returns

Returns a vector containing the predictive asymmetry for each value of ηs.

Normalization (hypothesis test)

If normalize == true (the default), then compute the normalized predictive asymmetry 𝒜. In this case, for each $\eta$ in ηs, compute 𝒜(η) by normalizing 𝔸(η) to some fraction f of the mean transfer entropy over prediction lags $-\eta, ..., \eta$ (exluding lag 0). Haaga et al. (2020) uses a normalization with f=1.0 as a built-in hypothesis test, avoiding more computationally costly surrogate testing.

Estimators

Any estimator that works for transferentropy will also work with predictive_asymmetry. Check the online documentation for compatiable estimators.

Examples

using CausalityTools
# Some example time series
x, y = rand(100), rand(100)
# 𝔸(x → y) over prediction lags 1:5
𝔸reg  = predictive_asymmetry(x, y, VisitationFrequency(RectangularBinning(5)), 1:5)

Experimental!

This is a method that does not yet appear in a peer-reviewed scientific journal. Feel free to use, but consider it experimental for now. It will reappear in a 2.X release in new form once published in a peer-reviewed journal.

source

`PATest`

CausalityTools.PATest — Type

PATest <: IndependenceTest
PATest(measure::PA, est)

A test for directional (conditional) dependence based on the modified PA measure, estimated using the given estimator est. Compatible estimators are listed in the docstring for PA.

When used with independence, a PATestResult summary is returned.

Note

This is an experimental test. It is part of an ongoing paper submission revision, but is provided here for convenience.

source

CausalityTools.PATestResult — Type

PATestResult(n_vars, ΔA, ttest, pvalue)

Holds the result of a SurrogateTest. n_vars is the number of variables used for the test (2 for pairwise, 3 for conditional). ΔA is the distribution of asymmetries, one for each η. ttest is a one-sample t-test, and pvalue is the right-tailed p-value for the test.

source