R/chart.QQPlot.R

In guillermozbta/portafolio-master: Econometric tools for performance and risk analysis.

#' Plot a QQ chart
#' 
#' Plot the return data against any theoretical distribution.
#' 
#' A Quantile-Quantile (QQ) plot is a scatter plot designed to compare the data
#' to the theoretical distributions to visually determine if the observations
#' are likely to have come from a known population. The empirical quantiles are
#' plotted to the y-axis, and the x-axis contains the values of the theorical
#' model.  A 45-degree reference line is also plotted. If the empirical data
#' come from the population with the choosen distribution, the points should
#' fall approximately along this reference line. The larger the departure from
#' the reference line, the greater the evidence that the data set have come
#' from a population with a different distribution.
#' 
#' @param R an xts, vector, matrix, data frame, timeSeries or zoo object of
#' asset returns
#' @param distribution root name of comparison distribution - e.g., 'norm' for
#' the normal distribution; 't' for the t-distribution. See examples for other
#' ideas.
#' @param xlab set the x-axis label, as in \code{\link{plot}}
#' @param ylab set the y-axis label, as in \code{\link{plot}}
#' @param xaxis if true, draws the x axis
#' @param yaxis if true, draws the y axis
#' @param ylim set the y-axis limits, same as in \code{\link{plot}}
#' @param main set the chart title, same as in \code{plot}
#' @param las set the direction of axis labels, same as in \code{plot}
#' @param envelope confidence level for point-wise confidence envelope, or
#' FALSE for no envelope.
#' @param labels vector of point labels for interactive point identification,
#' or FALSE for no labels.
#' @param col color for points and lines; the default is the \emph{second}
#' entry in the current color palette (see 'palette' and 'par').
#' @param lwd set the line width, as in \code{\link{plot}}
#' @param pch symbols to use, see also \code{\link{plot}}
#' @param cex symbols to use, see also \code{\link{plot}}
#' @param line 'quartiles' to pass a line through the quartile-pairs, or
#' 'robust' for a robust-regression line; the latter uses the 'rlm' function
#' in the 'MASS' package. Specifying 'line = "none"' suppresses the line.
#' @param element.color provides the color for drawing chart elements, such as
#' the box lines, axis lines, etc. Default is "darkgray"
#' @param cex.legend The magnification to be used for sizing the legend
#' relative to the current setting of 'cex'
#' @param cex.axis The magnification to be used for axis annotation relative to
#' the current setting of 'cex'
#' @param cex.lab The magnification to be used for x- and y-axis labels
#' relative to the current setting of 'cex'
#' @param cex.main The magnification to be used for the main title relative to
#' the current setting of 'cex'.
#' @param \dots any other passthru parameters to the distribution function
#' 
#' @author John Fox, ported by Peter Carl
#' @seealso 
#' \code{\link[stats]{qqplot}} \cr 
#' \code{\link[car]{qq.plot}} \cr
#' \code{\link{plot}}
#' @references main code forked/borrowed/ported from the excellent: \cr Fox,
#' John (2007) \emph{car: Companion to Applied Regression} \cr
#' \url{http://www.r-project.org},
#' \url{http://socserv.socsci.mcmaster.ca/jfox/}
#' @keywords ts multivariate distribution models hplot
#' @examples
#' 
#' library(MASS)
#' data(managers)
#' 
#' x = checkData(managers[,2, drop = FALSE], na.rm = TRUE, method = "vector")
#' 
#' #layout(rbind(c(1,2),c(3,4)))
#' 
#' # Panel 1, Normal distribution
#' chart.QQPlot(x, main = "Normal Distribution", distribution = 'norm', envelope=0.95)
#' # Panel 2, Log-Normal distribution
#' fit = fitdistr(1+x, 'lognormal')
#' chart.QQPlot(1+x, main = "Log-Normal Distribution", envelope=0.95, distribution='lnorm')
#' #other options could include
#' #, meanlog = fit$estimate[[1]], sdlog = fit$estimate[[2]])
#' 
#' \dontrun{
#' # Panel 3, Skew-T distribution
#' library(sn)
#' fit = st.mle(y=x)
#' chart.QQPlot(x, main = "Skew T Distribution", envelope=0.95, 
#'              distribution = 'st', location = fit$dp[[1]], 
#'              scale = fit$dp[[2]], shape = fit$dp[[3]], df=fit$dp[[4]])
#' 
#' #Panel 4: Stable Parietian
#' library(fBasics)
#' fit.stable = stableFit(x,doplot=FALSE)
#' chart.QQPlot(x, main = "Stable Paretian Distribution", envelope=0.95, 
#'              distribution = 'stable', alpha = fit(stable.fit)$estimate[[1]], 
#'              beta = fit(stable.fit)$estimate[[2]], gamma = fit(stable.fit)$estimate[[3]], 
#'              delta = fit(stable.fit)$estimate[[4]], pm = 0)
#' }
#' #end examples
#' 
#' @export 
chart.QQPlot <-
function(R, distribution="norm", ylab=NULL,
        xlab=paste(distribution, "Quantiles"), main=NULL, las=par("las"),
        envelope=FALSE, labels=FALSE, col=c(1,4), lwd=2, pch=1, cex=1,
        line=c("quartiles", "robust", "none"), element.color = "darkgray", 
        cex.axis = 0.8, cex.legend = 0.8, cex.lab = 1, cex.main = 1, xaxis=TRUE, yaxis=TRUE, ylim=NULL, ...)
{ # @author Peter Carl

    # DESCRIPTION:
    # A wrapper to create a chart of relative returns through time

    # Inputs:
    # R: a matrix, data frame, or timeSeries of returns

    # Outputs:
    # A Normal Q-Q Plot

    # FUNCTION:

    x = checkData(R, method = "vector", na.rm = TRUE)
#     n = length(x)

    if(is.null(main)){ 
        if(!is.null(colnames(R)[1])) 
            main=colnames(R)[1]
        else
            main = "QQ Plot"
    }
    if(is.null(ylab)) ylab = "Empirical Quantiles"
    # the core of this function is taken from John Fox's qq.plot, which is part of the car package
    result <- NULL
    line <- match.arg(line)
    good <- !is.na(x)
    ord <- order(x[good])
    ord.x <- x[good][ord]
    q.function <- eval(parse(text=paste("q",distribution, sep="")))
    d.function <- eval(parse(text=paste("d",distribution, sep="")))
    n <- length(ord.x)
    P <- ppoints(n)
    z <- q.function(P, ...)
    plot(z, ord.x, xlab=xlab, ylab=ylab, main=main, las=las, col=col[1], pch=pch,
        cex=cex, cex.main = cex.main, cex.lab = cex.lab, axes=FALSE, ylim=ylim, ...)
    if (line=="quartiles"){
        Q.x<-quantile(ord.x, c(.25,.75))
        Q.z<-q.function(c(.25,.75), ...)
        b<-(Q.x[2]-Q.x[1])/(Q.z[2]-Q.z[1])
        a<-Q.x[1]-b*Q.z[1]
        abline(a, b, col=col[2], lwd=lwd)
        }
    if (line=="robust"){
        stopifnot("package:MASS" %in% search() || require("MASS",quietly=TRUE))
        coef<-coefficients(rlm(ord.x~z))
        a<-coef[1]
        b<-coef[2]
        abline(a,b, col=col[2])
        }
    if (line != 'none' & envelope != FALSE) {
        zz<-qnorm(1-(1-envelope)/2)
        SE<-(b/d.function(z, ...))*sqrt(P*(1-P)/n)
        fit.value<-a+b*z
        upper<-fit.value+zz*SE
        lower<-fit.value-zz*SE
        lines(z, upper, lty=2, lwd=lwd/2, col=col[2])
        lines(z, lower, lty=2, lwd=lwd/2, col=col[2])
        }
    if (labels[1]==TRUE & length(labels)==1) labels<-seq(along=z)
    if (labels[1] != FALSE) {
        selected<-identify(z, ord.x, labels[good][ord])
        result <- seq(along=x)[good][ord][selected]
        }
    if (is.null(result)) invisible(result) else sort(result)

#     if(distribution == "normal") {
#         if(is.null(xlab)) xlab = "Normal Quantiles"
#         if(is.null(ylab)) ylab = "Empirical Quantiles"
#         if(is.null(main)) main = "Normal QQ-Plot"
# 
#         # Normal Quantile-Quantile Plot:
#         qqnorm(x, xlab = xlab, ylab = ylab, main = main, pch = symbolset, axes = FALSE, ...)
# #         qqline(x, col = colorset[2], lwd = 2)
#         q.theo = qnorm(c(0.25,0.75))
#     }
#     if(distribution == "sst") {
#         library("sn")
#         if(is.null(xlab)) xlab = "Skew-T Quantiles"
#         if(is.null(ylab)) ylab = "Empirical Quantiles"
#         if(is.null(main)) main = "Skew-T QQ-Plot"
# 
#         # Skew Student-T Quantile-Quantile Plot:
#         y = qst(c(1:n)/(n+1))
#         qqplot(y, x, xlab = xlab, ylab = ylab, axes=FALSE, main=main, ...)
#         q.theo = qst(c(0.25,0.75))
#     }
#     if(distribution == "cauchy") {
#         if(is.null(xlab)) xlab = "Cauchy Quantiles"
#         if(is.null(ylab)) ylab = "Empirical Quantiles"
#         if(is.null(main)) main = "Cauchy QQ-Plot"
# 
#         # Skew Student-T Quantile-Quantile Plot:
#         y = qcauchy(c(1:n)/(n+1))
#         qqplot(y, x, xlab = xlab, ylab = ylab, axes=FALSE, main=main, ...)
#         q.theo = qcauchy(c(0.25,0.75))
#     }
#     if(distribution == "lnorm") {
#         if(is.null(xlab)) xlab = "Log Normal Quantiles"
#         if(is.null(ylab)) ylab = "Empirical Quantiles"
#         if(is.null(main)) main = "Log Normal QQ-Plot"
# 
#         # Skew Student-T Quantile-Quantile Plot:
#         y = qlnorm(c(1:n)/(n+1))
#         qqplot(y, x, xlab = xlab, ylab = ylab, axes=FALSE, main=main, ...)
#         q.theo = qlnorm(c(0.25,0.75))
#     }
# 
#     q.data=quantile(x,c(0.25,0.75))
#     slope = diff(q.data)/diff(q.theo)
#     int = q.data[1] - slope* q.theo[1]
# 
#     if(line) abline(int, slope, col = colorset[2], lwd = 2)
    if(xaxis)
      axis(1, cex.axis = cex.axis, col = element.color)
    if(yaxis)
      axis(2, cex.axis = cex.axis, col = element.color)

    box(col=element.color)

}

###############################################################################
# R (http://r-project.org/) Econometrics for Performance and Risk Analysis
#
# Copyright (c) 2004-2014 Peter Carl and Brian G. Peterson
#
# This R package is distributed under the terms of the GNU Public License (GPL)
# for full details see the file COPYING
#
# $Id$
#
###############################################################################