\name{ScalingLawPlot}
\alias{scalinglawPlot}


\title{Scaling law behaviour}

\description{

  Evaluates the scaling exponent of a financial return series and plots
  the scaling law.
    
}

\usage{
scalinglawPlot(x, span = ceiling(log(length(x)/252)/log(2)), doplot = TRUE, 
    labels = TRUE, trace = TRUE, \dots)
}

\arguments{

  \item{x}{
    an uni- or multivariate return 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{span}{
    an integer value, determines for the \code{qqgaussPlot} the 
    plot range, by default 5, and for the \code{scalingPlot} a
    reasonable number of points for the scaling range, by
    default daily data with 252 business days per year are
    assumed.
  }
  \item{doplot}{
    a logical value. Should a plot be displayed?
  }
  \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{trace}{
    a logical value. Should the computation be traced?
  }
  \item{\dots}{
    arguments to be passed.
  }
}

\value{
    
  a list with the following components:
  \item{Intercept}{intercept,}
  \item{Exponent}{the scaling exponent,}
  \item{InverseExponent}{the inverse of the scaling component.}
    
}

\details{
    
  \bold{Scaling Behavior:}
  \cr\cr
  The function \code{scalingPlot} plots the scaling law of financial 
  time series under aggregation and returns an estimate for the scaling 
  exponent. The scaling behavior is a very striking effect of the 
  foreign exchange market and also other markets expressing a regular
  structure for the volatility. Considering the average absolute
  return over individual data periods one finds a scaling power law
  which relates the mean volatility over given time intervals
  to the size of these intervals. The power law is in many cases 
  valid over several orders of magnitude in time. Its exponent  
  usually deviates significantly from a Gaussian random walk model 
  which implies 1/2. 
  
}

\references{

Taylor S.J. (1986); 
    \emph{Modeling Financial Time Series},
    John Wiley and Sons, Chichester.
    
}

\author{
  Diethelm Wuertz for the Rmetrics \R-port.
}

\examples{   
## data - 
   data(LPP2005REC, package = "timeSeries")
   SPI <- LPP2005REC[, "SPI"]
   plot(SPI, type = "l", col = "steelblue", main = "SP500")
   abline(h = 0, col = "grey")

## teffectPlot -
   # Scaling Law Effect:
   scalinglawPlot(SPI)
}

\keyword{hplot}
