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\name{ExtremesPreprocessing}
\alias{ExtremesPreprocessing}
\alias{findThreshold}
\alias{blocks}
\alias{blockMaxima}
\alias{deCluster}
\title{Preprocessing Extreme Value Data}
\description{
A collection and description of functions for preprocessing
data for extreme value analysis. Included are tools to
separate data beyond a threshold value, to compute blockwise
data like block maxima, and to decluster point process data.
\cr
The functions are:
\tabular{ll}{
\code{findThreshold} \tab Upper threshold for a given number of extremes, \cr
\code{blocks} \tab Create data blocks on vectors and time series, \cr
\code{blockMaxima} \tab Block Maxima from a vector or a time series, \cr
\code{deCluster} \tab Declusters clustered point process data. }
}
\usage{
findThreshold(x, n = NA)
blocks(x, block = "month", FUN = max)
blockMaxima(x, block = "month", details = FALSE, doplot = TRUE, \dots)
deCluster(x, run = NA, doplot = TRUE)
}
\arguments{
\item{block}{
the block size. A numeric value is interpreted as the number
of data values in each successive block. All the data is used,
so the last block may not contain \code{block} observations.
If the \code{data} has a \code{times} attribute containing (in
an object of class \code{"POSIXct"}, or an object that can be
converted to that class, see \code{\link{as.POSIXct}}) the
times/dates of each observation, then \code{block} may instead
take the character values \code{"month"}, \code{"quarter"},
\code{"semester"} or \code{"year"}. By default monthly blocks
from daily data are assumed.
}
\item{details}{
[blockMaxima] - \cr
a logical. Should details be printed?
}
\item{doplot}{
a logical. Should the results be plotted?
}
\item{FUN}{the function to be applied. Additional arguments are
passed by the \code{\dots} argument.
}
\item{n}{
[findThreshold] - \cr
a numeric value or vector giving number of extremes above
the threshold. If \code{n} is not specified, \code{n} is
set to an integer representing 5\% of the data from the
whole data set \code{x}.
}
\item{run}{
[deCluster] - \cr
parameter to be used in the runs method; any two consecutive
threshold exceedances separated by more than this number of
observations/days are considered to belong to different clusters.
}
\item{x}{
a numeric data vector from which \code{findThreshold} and
\code{blockMaxima} determine the threshold values and block
maxima values.
For the function \code{deCluster} the argument
\code{x} represents a numeric vector of threshold exceedances
with a \code{times} attribute which should be a numeric
vector containing either the indices or the times/dates
of each exceedance (if times/dates, the attribute should
be an object of class \code{"POSIXct"} or an object that
can be converted to that class; see \code{\link{as.POSIXct}}).
}
\item{\dots}{
additional arguments passed to the FUN or plot function.
}
}
\details{
\bold{Finding Thresholds:}
\cr\cr
The function \code{findThreshold} finds a threshold so that a given
number of extremes lie above. When the data are tied a threshold is
found so that at least the specified number of extremes lie above.
\cr
\bold{Computing Block Maxima:}
\cr\cr
The function \code{blockMaxima} calculates block maxima from a vector
or a time series, whereas the function
\code{blocks} is more general and allows for the calculation of
an arbitrary function \code{FUN} on blocks.
\cr
\bold{De-Clustering Point Processes:}
\cr\cr
The function \code{deCluster} declusters clustered point process
data so that Poisson assumption is more tenable over a high threshold.
}
\value{
\code{findThreshold}
\cr
returns a numeric vector of suitable thresholds.
\code{blockMaxima}
\cr
returns a numeric vector of block maxima data.
\code{deCluster}
\cr
returns an object for the declustered point process.
}
\references{
Embrechts, P., Klueppelberg, C., Mikosch, T. (1997);
\emph{Modelling Extremal Events},
Springer Verlag.
}
\seealso{
\code{\link{MdaPlots}},
\code{\link{ExtremeIndexPlots}},
\code{\link{GpdFit}},
\code{\link{PotFit}}.
}
\examples{
## findThreshold -
xmpExtremes("\nStart: Find Thresold >")
# Find threshold giving (at least) fifty exceedances
# for Danish Fire data
data(danish)
findThreshold(danish, n = c(10, 50, 100))
## blockMaxima -
xmpExtremes("\nNext: Compute Block Maxima >")
# Block Maxima (Minima) for the right and left tails
# of the BMW log returns:
data(bmw)
par(mfrow = c(2, 1))
blockMaxima( bmw, block = 100)
blockMaxima(-bmw, block = 100)
## deCluster -
xmpExtremes("\nNext: De-Cluster Exceedences >")
# Decluster the 200 exceedances of a particular
# threshold in the negative BMW log-return data
par(mfrow = c(2, 2))
fit = potFit(-bmw, nextremes = 200)
deCluster(fit$fit$data, 30)
}
\keyword{data}
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