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Surrogate methods

Iterated amplitude-adjusted Fourier transform (iAAFT) surrogates

# TimeseriesSurrogates.iaaft — Function.

iaaft(a::AbstractArray{Number, 2}; cols = 1:size(d, 2))

Iterated amplitude-adjusted Fourier transform (IAAFT) surrogate of an array, where each column is a scalar-valued time series. cols controls which variables of the embedding are shuffled.

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iaaft(E::Embeddings.AbstractEmbedding; cols = 1:size(E.points, 1))

Column-wise iterated amplitude-adjusted Fourier transform (IAAFT) surrogate of an embedding. cols controls which variables of the embedding are shuffled.

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iaaft(d::DynamicalSystemsBase.Dataset; cols = 1:size(d, 2))

Iterated amplitude-adjusted Fourier transform (IAAFT) surrogate of a Dataset. cols controls which variables of the embedding are shuffled.

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Examples

Example 1

npts = 200
ts = sin.(diff(rand(npts + 1)))*0.5 .+ cos.(LinRange(0, 14*pi, npts))
p1 = plot(ts, label = "ts", lc = :black)
p2 = plot(iaaft(ts), label = "iaaft(ts)", xlabel = "Time step")
plot(p1, p2, layout = (2, 1))
ylabel!("Value");

Example 2

This gif shows iAAFT surrogate realizations for an cyclostationary AR2 (NSAR2) process (nsar2) from [1].

Example 3

This gif shows iAAFT surrogate realizations for an AR1 process.

References

  1. Lucio et al., Phys. Rev. E 85, 056202 (2012), after J. Timmer, Phys. Rev. E 58, 5153 (1998). https://journals.aps.org/pre/abstract/10.1103/PhysRevE.85.056202