#' 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
#' @author For QQplot with mixture normal distribution, Ke Li \email{kirkli@@stat.washington.edu}
#' @seealso
#' \code{\link[stats]{qqplot}} \cr
#' \code{\link[car]{qq.plot}} \cr
#' \code{\link{plot}} \cr
#' CRAN package \code{\link[nor1mix]{norMixFit}} for mixture normal distribution
#' @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)
#,
#,Panel 5: Mixture Normal distribution
#,chart.QQPlot(x, main = "Normal Mixture Distribution",
#, line=c("quartiles"), para=list(m=2), distribution = 'mixnormal',
#, envelope=0.95)
#,}
#'
#' #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]
n <- length(ord.x)
P <- ppoints(n)
if(distribution=="mixnormal")
{
qmixnormal <- function(q, ...){
# norMix distribution
para=list(...)$para
if(!is.list(para))stop(" 'para' must be a 'list' object")
if(is.null(para$m)|is.na(para$m))
stop("The number of component must be specified in 'para$m'")
require(nor1mix)
out = norMixEM(x, para$m, trace=0)
if (length(q)!=2){
# only print once
print("fitted model:")
print(out[1:para$m,],digits=3)
}
if(is.null(para$mu) | is.null(para$sig2))
# using fitted distribution
{
if (length(q)!=2)
print("using fitted model as theoretical distribution")
obj <- out
} else{
# using specified distribution
if(length(para$mu)!=para$m | length(para$sig2)!=para$m)
stop("the number of components mismatch with parameter inputs")
obj <- norMix(mu = para$mu, sig2 = para$sig2, w = para$w)
}
qnorMix(q,obj)
}
dmixnormal<- function(p, ...){
# norMix distribution
para=list(...)$para
if(!is.list(para))stop(" 'para' must be a 'list' object")
if(is.null(para$m)|is.na(para$m))
stop("The number of component must be specified in 'para$m'")
library(nor1mix)
out = norMixEM(x, para$m, trace=0)
if(is.null(para$mu) | is.null(para$sig2))
# using fitted distribution
{
obj <- out
} else{
# using specified distribution
if(length(para$mu) != para$m | length(para$sig2) != para$m)
stop("the number of components mismatch with parameter inputs")
obj <- norMix(mu = para$mu, sig2 = para$sig2, w = para$w)
}
dnorMix(p,obj)
}
}
q.function <- eval(parse(text=paste("q",distribution, sep="")))
d.function <- eval(parse(text=paste("d",distribution, sep="")))
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: chart.QQPlot.R 3301 2014-01-18 15:26:12Z braverock $
#
###############################################################################
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