PerformanceAnalytics (version 2.0.8)

chart.QQPlot: Plot a QQ chart

Description

Plot the return data against any theoretical distribution.

Usage

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,
  distributionParameter = 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

distributionParameter

a string of the parameters of the distribution e.g., distributionParameter = 'location = 1, scale = 2, shape = 3, df = 4' for skew-T distribution

...

any other passthru parameters to the distribution function

Author

John Fox, ported by Peter Carl

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
https://socserv.socsci.mcmaster.ca/jfox/

See Also

qqplot
qq.plot
plot

Examples

# you'll need lots of extra packages to run these examples of different distributions
if (FALSE)  # these examples require multiple packages from 'Suggests', so don't test on CRAN
library(MASS) 
library(PerformanceAnalytics)
data(managers)
x = checkData(managers[,2, drop = FALSE], na.rm = TRUE, method = "vector")

# Panel 1: Normal distribution
chart.QQPlot(x, main = "Normal Distribution",
		line=c("quartiles"), 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',distributionParameter='meanlog = fit$estimate[[1]], 
    sdlog = fit$estimate[[2]]')
 
# Panel 3: Mixture Normal distribution
# library(nor1mix)
obj = norMixEM(x,m=2)
chart.QQPlot(x, main = "Normal Mixture Distribution",
		line=c("quartiles"), distribution = 'norMix',  distributionParameter='obj',
		envelope=0.95)


# Panel 4: Symmetric t distribution
library(sn)
n = length(x)
fit.tSN = st.mple(as.matrix(rep(1,n)),x,symmetr = TRUE)
names(fit.tSN$dp) = c("location","scale","dof")
round(fit.tSN$dp,3)

chart.QQPlot(x, main = "MO Symmetric t-Distribution QQPlot",
		xlab = "quantilesSymmetricTdistEst",line = c("quartiles"),
		envelope = .95, distribution = 't', 
		distributionParameter='df=fit.tSN$dp[3]',pch = 20)

# Panel 5: Skewed t distribution
fit.st = st.mple(as.matrix(rep(1,n)),x)
# fit.st = st.mple(y=x)  Produces same result as line above
names(fit.st$dp) = c("location","scale","skew","dof")
round(fit.st$dp,3)

chart.QQPlot(x, main = "MO Returns Skewed t-Distribution QQPlot",
		xlab = "quantilesSkewedTdistEst",line = c("quartiles"),
		envelope = .95, distribution = 'st',
		distributionParameter = 'xi = fit.st$dp[1],
				omega = fit.st$dp[2],alpha = fit.st$dp[3],
				nu=fit.st$dp[4]',
		pch = 20)

# Panel 6: Stable Parietian
library(fBasics)
fit.stable = stableFit(x,doplot=FALSE)
chart.QQPlot(x, main = "Stable Paretian Distribution", envelope=0.95, 
             distribution = 'stable', 
             distributionParameter = '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