Plot a QQ chart

Plot the return data against any theoretical distribution.

chart.QQPlot(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,
  ...)

Arguments

R	an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns
distribution	root name of comparison distribution - e.g., 'norm' for the normal distribution; 't' for the t-distribution. See examples for other ideas.
ylab	set the y-axis label, as in plot
xlab	set the x-axis label, as in plot
main	set the chart title, same as in plot
las	set the direction of axis labels, same as in plot
envelope	confidence level for point-wise confidence envelope, or FALSE for no envelope.
labels	vector of point labels for interactive point identification, or FALSE for no labels.
col	color for points and lines; the default is the second entry in the current color palette (see 'palette' and 'par').
lwd	set the line width, as in plot
pch	symbols to use, see also plot
cex	symbols to use, see also plot
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.
element.color	provides the color for drawing chart elements, such as the box lines, axis lines, etc. Default is "darkgray"
cex.axis	The magnification to be used for axis annotation relative to the current setting of 'cex'
cex.legend	The magnification to be used for sizing the legend relative to the current setting of 'cex'
cex.lab	The magnification to be used for x- and y-axis labels relative to the current setting of 'cex'
cex.main	The magnification to be used for the main title relative to the current setting of 'cex'.
xaxis	if true, draws the x axis
yaxis	if true, draws the y axis
ylim	set the y-axis limits, same as in plot
…	any other passthru parameters to the distribution function

Details

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.

References

main code forked/borrowed/ported from the excellent: Fox, John (2007) car: Companion to Applied Regression http://socserv.socsci.mcmaster.ca/jfox/

See also

qqplot qq.plot plot

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]])

# NOT RUN {
# 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