# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Library General Public
# License as published by the Free Software Foundation; either
# version 2 of the License, or (at your option) any later version.
#
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 
# GNU Library General Public License for more details.
#
# You should have received a copy of the GNU Library General 
# Public License along with this library; if not, write to the 
# Free Foundation, Inc., 59 Temple Place, Suite 330, Boston, 
# MA  02111-1307  USA

# Copyrights (C)
# for this R-port: 
#   1999 - 2008, Diethelm Wuertz, Rmetrics Foundation, GPL
#   Diethelm Wuertz <wuertz@itp.phys.ethz.ch>
#   www.rmetrics.org
# for the code accessed (or partly included) from other R-ports:
#   see R's copyright and license files
# for the code accessed (or partly included) from contributed R-ports
# and other sources
#   see Rmetrics's copyright file


################################################################################
# FUNCTION:             DESCRIPTION:
#  scalinglawPlot        Evaluates and displays scaling law behavior
################################################################################


scalinglawPlot =
function(x, span = ceiling(log(length(x)/252)/log(2)), doplot = TRUE, 
labels = TRUE, trace = TRUE, ...)
{   # A function implemented by Diethelm Wuertz
  
    # Description:
    #   Investigates the scaling law.
    #   The input "x" requires log-returns.
 
    # Arguments:
    #   x - an uni- or multivariate return series of class 'timeSeries' 
    #       or any other object which can be transformed by the function
    #       'as.timeSeries()' into an object of class 'timeSeries'.
    #   labels - a logical flag, by default true. Should a default 
    #       main title and labels addet to the plot?
    
    # FUNCTION: 
    
    # Settings:
    if (!is.timeSeries(x)) x = as.timeSeries(x)
    Units = colnames(x)
    
    # Labels:
    if (labels) {
        main = "Scaling Law Plot"
        xlab = "log-time"
        ylab = "log-volatility"
    } else {
        main = xlab = ylab = ""
    }
    
    X = x
    DIM = dim(X)[2]
    Intercept = Exponent = InverseExponent = NULL
    for (i in 1:DIM) {
        
        # Get Data:
        x = as.vector(X@Data[, i])
        if (labels) main = Units[i]
    
    
        # Settings:
        logtimesteps = span
        xmean = mean(x)
        
        # x have to be logarithmic returns
        y = (x-xmean)
        logprices = cumsum(y)
        
        # Scaling Power Low:
        scale = function (nx, logprices) {
            sum(abs(diff(logprices, lag = (2^nx))))}     
        nx = 0:logtimesteps; x = nx*log(2)
        y = log(apply(matrix(nx), 1, scale, logprices))
        # fit = lsfit(x, y)$coefficients
        
        # Runs in both environments, R and SPlus:
        fit = lsfit(x, y)
        
        # Robust Fit:       
        # fit = l1fit(x, y) 
        
        # Fit Result:
        Fit = unlist(fit)[1:2]
        alpha = 1.0/Fit[2]
        if (doplot) { 
            plot(x, y, main = main, xlab = xlab, ylab = ylab, ...)
            abline(Fit[1], Fit[2])
            abline(Fit[1], 0.5, col = "steelblue") 
        }
        if (labels) grid()
        
        # Trace:
        if (trace) {
            cat ("\nScaling Law:         ", Units[i])
            cat ("\n  Plot Intercept     ", fit$coefficients[1])
            cat ("\n  Plot Slope         ", fit$coefficients[2])
            cat ("\n  Plot Inverse Slope ", 1/fit$coefficients[2])
            cat ("\n\n") 
        } 
        Intercept = c(Intercept, fit$coefficients[1])
        Exponent = c(Exponent, fit$coefficients[2])
        InverseExponent = c(InverseExponent, 1/fit$coefficients[2])
        
    }
    
    names(Intercept) = Units
    names(Exponent) = Units
    names(InverseExponent) = Units
    result = list(
        Intercept = Intercept, 
        Exponent = Exponent, 
        InverseExponent = InverseExponent)
        
    # Return Value:
    invisible(result)
}


################################################################################