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\name{acfPlot}
\alias{acfPlot}
\alias{pacfPlot}
\alias{teffectPlot}
\alias{lacfPlot}
\concept{acf}
\concept{autocorrelation}
\concept{pacf}
\concept{partial autocorrelation}
\concept{Taylor effect plot}
\title{Autocorrelation function plots}
\description{
Produce plots of the autocorrelation function (ACF), the partial ACF,
the lagged ACF, and the Taylor effect plot.
}
\usage{
acfPlot(x, labels = TRUE, \dots)
pacfPlot(x, labels = TRUE, \dots)
lacfPlot(x, n = 12, lag.max = 20, type = c("returns", "values"),
labels = TRUE, \dots)
teffectPlot(x, deltas = seq(from = 0.2, to = 3, by = 0.2), lag.max = 10,
ymax = NA, standardize = TRUE, labels = TRUE, \dots)
}
\arguments{
\item{x}{
an uni- or multivariate time series of class \code{"timeSeries"} or
any other object which can be transformed by the function
\code{as.timeSeries()} into an object of class \code{"timeSeries"}.
}
\item{labels}{
a logical value, whether or not x- and y-axes should be
automatically labeled and a default main title should be added to
the plot. By default \code{TRUE}.
}
\item{n}{
an integer value, the number of lags.
}
\item{lag.max}{
maximum lag for which the autocorrelation should be calculated, an
integer.
}
\item{type}{
a character string which specifies the type of the input series,
either \code{"returns"} or \code{"values"}. In the case of a return
series as input, the required value series is computed by cumulating
the financial returns: \code{exp(colCumsums(x))}
}
\item{deltas}{
the exponents, a numeric vector, by default ranging from 0.2 to 3.0
in steps of 0.2.
}
\item{ymax}{
maximum y-axis value on plot. If \code{NA}, then the value is
selected automatically.
}
\item{standardize}{
a logical value. Should the vector \code{x} be standardized?
}
\item{\dots}{
arguments to be passed.
}
}
\details{
The following plots are described here:
\tabular{ll}{
\code{acfPlot} \tab autocorrelation function plot, \cr
\code{pacfPlot} \tab partial autocorrelation function plot, \cr
\code{lacfPlot} \tab lagged autocorrelation function plot, \cr
\code{teffectPlot} \tab Taylor effect plot.}
\subsection{Autocorrelation Functions}{
The functions \code{acfPlot} and \code{pacfPlot}, plot and estimate
autocorrelation and partial autocorrelation function. The functions
allow to get a first view on correlations within the time series.
The functions are synonym function calls for R's \code{acf} and
\code{pacf} from the the \code{ts} package.
}
\subsection{Taylor Effect}{
The "Taylor Effect" describes the fact that absolute returns of
speculative assets have significant serial correlation over long
lags. Even more, autocorrelations of absolute returns are typically
greater than those of squared returns. From these observations the
Taylor effect states, that that the autocorrelations of absolute
returns to the the power of \code{delta},
\code{abs(x-mean(x))^delta} reach their maximum at \code{delta = 1}.
The function \code{teffect} explores this behaviour. A plot is
created which shows for each lag (from 1 to \code{max.lag}) the
autocorrelations as a function of the exponent \code{delta}. In the
case that the above formulated hypothesis is supported, all the
curves should peak at the same value around \code{delta = 1}.
}
}
\value{
for \code{acfPlot} and \code{pacfplot},
an object of class \code{"acf"}, see \code{\link{acf}};
for \code{teffectPlot}, a numeric matrix
of order \code{deltas} by \code{max.lag} with
the values of the autocorrelations;
for \code{lacfPlot}, a list with the following two elements:
\item{Rho}{the autocorrelation function,}
\item{lagged}{the lagged correlations.}
}
\references{
Taylor S.J. (1986);
\emph{Modeling Financial Time Series},
John Wiley and Sons, Chichester.
Ding Z., Granger C.W.J., Engle R.F. (1993);
\emph{A long memory property of stock market returns and a new model},
Journal of Empirical Finance 1, 83.
}
\seealso{
\code{\link{seriesPlot}},
\code{\link{returnPlot}},
\code{\link{cumulatedPlot}},
\code{\link{drawdownPlot}}
\code{\link{qqnormPlot}},
\code{\link{qqnigPlot}},
\code{\link{qqghtPlot}},
\code{\link{qqgldPlot}}
\code{\link{histPlot}},
\code{\link{densityPlot}},
\code{\link{logDensityPlot}}
\code{\link{boxPlot}},
\code{\link{boxPercentilePlot}}
\code{\link{scalinglawPlot}}
\code{\link{returnSeriesGUI}}
}
\examples{
## data
data(LPP2005REC, package = "timeSeries")
SPI <- LPP2005REC[, "SPI"]
plot(SPI, type = "l", col = "steelblue", main = "SP500")
abline(h = 0, col = "grey")
## Taylor Effect:
teffectPlot(SPI)
}
\keyword{hplot}
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