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\name{surrogate}
\alias{surrogate}
\title{Generate Surrogate Data and Statistics}
\description{
Generates \code{ns} surrogate samples from the original data \code{x}
and computes the standard error and the bias of \code{statistic} as in
a bootstrap setup, if \code{statistic} is given.
}
\usage{
surrogate(x, ns = 1, fft = FALSE, amplitude = FALSE,
statistic = NULL, \dots)
}
\arguments{
\item{x}{a numeric vector or time series.}
\item{ns}{the number of surrogate series to compute.}
\item{fft}{a logical indicating whether phase randomized surrogate
data is generated.}
\item{amplitude}{a logical indicating whether amplitude-adjusted
surrogate data is computed.}
\item{statistic}{a function which when applied to a time series
returns a vector containing the statistic(s) of interest.}
\item{\dots}{Additional arguments for \code{statistic} which are
passed unchanged each time it is called.}
}
\details{
If \code{fft} is \code{FALSE}, then \code{x} is mixed in temporal
order, so that all temporal dependencies are eliminated, but the
histogram of the original data is preserved. If \code{fft} is
\code{TRUE}, then surrogate data with the same spectrum as \code{x} is
computed by randomizing the phases of the Fourier coefficients of
\code{x}. If in addition \code{amplitude} is \code{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.
}
\value{
If \code{statistic} is \code{NULL}, then it returns a matrix or time
series with \code{ns} columns and \code{length(x)} rows containing the
surrogate data. Each column contains one surrogate sample.
If \code{statistic} is given, then a list of class
\code{"resample.statistic"} with the following elements is returned:
\item{statistic}{the results of applying \code{statistic} to each of
the simulated time series.}
\item{orig.statistic}{the results of applying \code{statistic} to the
original series.}
\item{bias}{the bias of the statistics computed as in a bootstrap
setup.}
\item{se}{the standard error of the statistics computed as in a
bootstrap setup.}
\item{call}{the original call of \code{surrogate}.}
}
\references{
J. Theiler, B. Galdrikian, A. Longtin, S. Eubank, and J. D. Farmer
(1992): Using Surrogate Data to Detect
Nonlinearity in Time Series, in \emph{Nonlinear Modelling and
Forecasting}, Eds. M. Casdagli and S. Eubank, Santa Fe Institute,
Addison Wesley, 163--188.
}
\author{A. Trapletti}
\seealso{
\code{\link{sample}}, \code{\link{tsbootstrap}}
}
\examples{
x <- 1:10 # Simple example
surrogate(x)
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)
}
\keyword{ts}
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