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\name{bds.test}
\alias{bds.test}
\alias{print.bdstest}
\title{BDS Test}
\description{
Computes and prints the BDS test statistic for the null that \code{x}
is a series of i.i.d. random variables.
}
\usage{
bds.test(x, m = 3, eps = seq(0.5 * sd(x), 2 * sd(x), length.out = 4),
trace = FALSE)
}
\arguments{
\item{x}{a numeric vector or time series.}
\item{m}{an integer indicating that the BDS test statistic is computed
for embedding dimensions \code{2}, \dots, \code{m}.}
\item{eps}{a numeric vector of epsilon values for close points. The
BDS test is computed for each element of \code{eps}. It should be
set in terms of the standard deviation of \code{x}.}
\item{trace}{a logical indicating whether some informational output is
traced.}
}
\details{
This test examines the ``spatial dependence'' of the observed
series. To do this, the series is embedded in \code{m}-space and the
dependence of \code{x} is examined by counting ``near'' points.
Points for which the distance is less than \code{eps} are called
``near''. The BDS test statistic is asymptotically standard Normal.
Missing values are not allowed.
There is a special print method for objects of class \code{"bdstest"}
which by default uses 4 digits to format real numbers.
}
\value{
A list with class \code{"bdstest"} containing the following components:
\item{statistic}{the values of the test statistic.}
\item{p.value}{the p-values of the test.}
\item{method}{a character string indicating what type of test was
performed.}
\item{parameter}{a list with the components \code{m} and \code{eps}
containing the embedding dimensions and epsilon values for which the
statistic is computed.}
\item{data.name}{a character string giving the name of the data.}
}
\references{
J. B. Cromwell, W. C. Labys and M. Terraza (1994):
\emph{Univariate Tests for Time Series Models},
Sage, Thousand Oaks, CA, pages 32--36.
}
\author{B. LeBaron, Ported to R by A. Trapletti}
\examples{
x <- rnorm(100)
bds.test(x) # i.i.d. example
x <- c(rnorm(50), runif(50))
bds.test(x) # not identically distributed
x <- quadmap(xi = 0.2, a = 4.0, n = 100)
bds.test(x) # not independent
}
\keyword{ts}
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