Generate Surrogate Data and Statistics

Generates ns surrogate samples from the original data x and computes the standard error and the bias of statistic as in a bootstrap setup, if statistic is given.

surrogate(x, ns = 1, fft = FALSE, amplitude = FALSE,
          statistic = NULL, ...)
a numeric vector or time series.
the number of surrogate series to compute.
a logical indicating whether phase randomized surrogate data is generated.
a logical indicating whether amplitude-adjusted surrogate data is computed.
a function which when applied to a time series returns a vector containing the statistic(s) of interest.
Additional arguments for statistic which are passed unchanged each time it is called.

If fft is FALSE, then x is mixed in temporal order, so that all temporal dependencies are eliminated, but the histogram of the original data is preserved. If fft is TRUE, then surrogate data with the same spectrum as x is computed by randomizing the phases of the Fourier coefficients of x. If in addition amplitude is TRUE, then also the amplitude distribution of the original series is preserved.

Note, that the interpretation of the computed standard error and bias is different than in a bootstrap setup.

To compute the phase randomized surrogate and the amplitude adjusted data algorithm 1 and 2 from Theiler et al. (1992), pp. 183, 184 are used. Missing values are not allowed.


  • If statistic is NULL, then it returns a matrix or time series with ns columns and length(x) rows containing the surrogate data. Each column contains one surrogate sample.

    If statistic is given, then a list of class "resample.statistic" with the following elements is returned:

  • statisticthe results of applying statistic to each of the simulated time series.
  • orig.statisticthe results of applying statistic to the original series.
  • biasthe bias of the statistics computed as in a bootstrap setup.
  • sethe standard error of the statistics computed as in a bootstrap setup.
  • callthe original call of surrogate.


J. Theiler, B. Galdrikian, A. Longtin, S. Eubank, and J. D. Farmer (1992): Using Surrogate Data to Detect Nonlinearity in Time Series, in Nonlinear Modelling and Forecasting, Eds. M. Casdagli and S. Eubank, Santa Fe Institute, Addison Wesley, 163--188.

See Also

sample, tsbootstrap

  • surrogate
x <- 1:10  # Simple example

n <- 500  # Generate AR(1) process
e <- rnorm(n)  
x <- double(n)
x[1] <- rnorm(1)
for(i in 2:n) {
  x[i] <- 0.4 * x[i-1] + e[i]
x <- ts(x)

theta <- function(x)  # Autocorrelations up to lag 10
  return(acf(x, plot=FALSE)$acf[2:11])

surrogate(x, ns=50, fft=TRUE, statistic=theta)
Documentation reproduced from package tseries, version 0.10-1, License: GPL (see file COPYING)

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