Skip to content

Surrogate methods

Iterated amplitude-adjusted Fourier transform (iAAFT) surrogates

Valid inputs

iAAFT surrogates may be generated from the following inputs:

  • AbstractArray{T, 1} instances (scalar-valued data series)
  • AbstractArray{Number, 2} instances (multivarate scalar-valued data series), for which surrogates are generated column-wise.
  • Dataset instances from DynamicalSystems.jl, for which surrogates are generated column-wise.
  • Embedding instances, for which surrogates are generated variable-wise (row-wise on the points).

Documentation

# TimeseriesSurrogates.iaaft — Function.

iaaft(ts::AbstractArray{T, 1} where T;
        n_maxiter = 200, tol = 1e-6, n_windows = 50)

Generate an iteratively adjusted amplitude adjusted Fourier transform (IAAFT) [1] surrogate realization of ts.

Arguments

  • ts is the time series for which to generate an AAFT surrogate realization.
  • n_maxiter sets the maximum number of iterations to allow before ending the algorithm (if convergence is slow).
  • tol is the relative tolerance for deciding if convergence is achieved.
  • n_window is the number is windows used when binning the periodogram (used for determining convergence).

Literature references

  1. T. Schreiber; A. Schmitz (1996). "Improved Surrogate Data for Nonlinearity

Tests". Phys. Rev. Lett. 77 (4): 635–638. doi:10.1103/PhysRevLett.77.635. PMID 10062864.

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.

source

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.

source

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.

source