Surrogate method overview
The method of surrogate data is commonly used in the analysis of dynamical systems. For an overview of surrogate methods, see the recent review by Lancaster et al., 2018.
What is a surrogate realization?
A surrogate realization of a dataset is a dataset that is formed either by shuffling the values of the original dataset in a particular way. There are two main ways of creating the data: constrained realizations and typical realizations (Theiler & Prichard, 1996).
Constrained realizations
Constrained surrogate realizations are formed by shuffling the values of the input data series in a way that retains some property of the original data. For example, random shuffle surrogates (randomshuffle) retain the histogram of the data. AAFT surrogates (aaft) aim to preserve the periodogram of the original data series.
Typical realizations
Typical surrogate realizations are generated by first fitting a model to the input data, then generating new data from that model. Random phase Fourier surrogates (randomphases), for example, retain the amplitudes of the original data, but shuffles the phases.
Implemented algorithms
The following surrogate methods are implemented. Function documentation and basic examples are available from the menu. For more details and demonstrations, visit the TimeseriesSurrogates.jl documentation.
| Algorithm | Function | Type | Reference |
|---|---|---|---|
| Randomly shuffling the values of the dataset | randomshuffle |
Constrained | Theiler et al., 1992 |
| Fourier transform phase surrogates | randomphases |
Typical | |
| Fourier transform amplitude surrogates | randomamplitudes |
Typical | |
| Amplitude-adjusted Fourier transform surrogates (AAFT) | aaft |
Constrained | |
| Iterated amplitude-adjusted Fourier transform surrogates (iAAFT) | iaaft |
Constrained | Schreiber & Schmitz, 1996 |
References
Lancaster, G., Iatsenko, D., Pidde, A., Ticcinelli, V., & Stefanovska, A. (2018). Surrogate data for hypothesis testing of physical systems. Physics Reports. https://doi.org/10.1016/j.physrep.2018.06.001
Schreiber, T., & Schmitz, A. (1996). Improved surrogate data for nonlinearity tests. Physical Review Letters, 77(4), 635. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.77.635
Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., & Doyne Farmer, J. (1992). Testing for nonlinearity in time series: the method of surrogate data. Physica D: Nonlinear Phenomena. https://doi.org/10.1016/0167-2789(92)90102-S
Theiler, J., & Prichard, D. (1996). Constrained-realization Monte-Carlo method for hypothesis testing. Physica D: Nonlinear Phenomena, 94(4), 221–235. https://www.sciencedirect.com/science/article/pii/0167278996000504