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List of CausalityTests

Most time series causality statistics, although many are so-called non-parameteric, require the analyst to provide some parameters for their estimation. Outputs may be vastly different based on the parameters chosen for a test.

To systematically deal with this fact, we create estimator-specific composite types for the different causality statistics. Every estimator is represented by a composite types whose fields are the parameters of the test. A causality test is therefore uniquely defined by its parameters. Available causality tests are listed below.

The advantage of this type-based approach is that we can have a unified syntax to estimate time series causality statistics, using the causality(source::AbstractVector, target::AbstractVector, test::CausalityTest) method, which is all a beginner-user needs to learn. The output of a call to causality depends on which test is provided, but the input format is always the same: your time series, plus a causality test.

Distance based tests

• CrossMappingTest
• ConvergentCrossMappingTest
• JointDistanceDistributionTest
• JointDistanceDistributionTTest
• SMeasureTest

Entropy based tests

• VisitationFrequencyTest
• TransferOperatorGridTest
• ExactSimplexIntersectionTest
• ApproximateSimplexIntersectionTest
• NearestNeighbourMITest

Predictive asymmetry tests

• PredictiveAsymmetryTest
• NormalisedPredictiveAsymmetryTest

Applying the tests

All tests can be used to compute causality statistics on empirical scalar valued time series, uncertain time series and directly from dynamical systems through the causality method.

Low-level causality statistics and their different methods/estimators are described on the following pages:

• Predictive asymmetry
• Transfer entropy
• Cross mapping
• S-Measure
• Joint distance distribution

Schemes for uncertainty handling

If you want to apply a causality test to time series with uncertainties, you can combine any of the tests above with the provided uncertainty handling, subsampling and resampling schemes.

Why wrapper types for the parameters?

There may be many ways of estimating a particular causality statistic. For example, there are many transfer entropy estimators, for example

• VisitationFrequency, and
• NearestNeigboursMI

Their corresponding transferentropy methods accept different inputs:

• transferentropy(pts, vars::TEVars, ϵ::RectangularBinning, estimator::BinningTransferEntropyEstimator)
• transferentropy(pts, vars::TEVars, estimator::NearestNeighbourMI)

Wouldn't it be nice to be able to use the same syntax for both estimators? Or for five more estimators that quantify causality in different manners? Instead of providing test parameters directly to the methods (e.g. transferentropy) directly, we can create a test instance that contains all the test parameters.

• test_vf = VisitationFrequencyTest(binning = RectangularBinning(5), ηs = 1:5)
• test_nn = NearestNeighbourMITest(ηs = 1:5)

The causality function and its methods provide a common interface for testing causal hypotheses. For analysing time series, all you need to do is provide a source and a target. Then, choose one of the available causality tests to quantify the (directional) dynamical dependence between source and target. If your data are uncertain, you can use resampling schemes to deal with that.