fExtremes (version 201.10059)

ExtremeIndexPlots: Extremal Index Estimation

Description

A collection and description of functions to compute the extremal index by three different kind of methods, the blocks method, the reciprocal mean cluster size method, and the runs method. The functiona are: ll{ exindexPlot Calculate and Plot Theta(1,2,3), exindexesPlot Calculate Theta(1,2) and Plot Theta(1). }

Usage

exindexPlot(x, block = "month", start = 5, end = NA, plottype = c("thresh", 
    "K"), labels = TRUE, autoscale = TRUE, ...)
    
exindexesPlot(x, block = 20, quantiles = seq(0.990, 0.999, 0.001), 
    doplot = TRUE, ...)

Arguments

autoscale

[exindexPlot] - whether or not plot should be automatically scaled; if not, xlim and ylim graphical parameters may be entered.

block

the block size. A numeric value is interpreted as the number of data values in each successive block. All the data is used, so the last block may not contain block observations. If the x has

doplot

[exindexesPlot] - a logical, should the results be plotted?

labels

[exindexPlot] - whether or not axes should be labelled.

plottype

[exindexPlot] - whether plot is to be by increasing threshold (thresh) or increasing K value (K).

quantiles

[exindexesPlot] - a numeric vector of quantile values.

start, end

[exindexPlot] - start is the lowest value of K at which to plot a point, and end the highest value; K is the number of blocks in which a specified threshold is exceeded.

x

a numeric vector, note raw values are required, not block maxima.

...

additional arguments passed to the plot function.

Value

• exindexPlot returns a data frame of results with the following columns: N, K, un, theta2, and theta. A plot with K on the lower x-axis and threshold Values on the upper x-axis versus the extremal index is displayed. exindexesPlot returns a data.frame with four columns: thresholds, theta1, theta2, and theta3. A plot with quantiles on the x-axis and versus the extremal indexes is displayed.

authors

Alexander McNeil, for the exindexPlot function, and Diethelm Wuertz for the exindexesPlot function.

References

Embrechts, P., Klueppelberg, C., Mikosch, T. (1997); Modelling Extremal Events, Springer. Chapter 8, 413--429.

See Also

hillPlot, gevFit.

Examples

## Extremal Index for the right and left tails 
## of the BMW log returns:
   xmpExtremes("Start: Plot the Extremal Index >")
   data(bmw)
   par(mfrow = c(2, 2), cex = 0.7)
   exindexPlot( bmw, block = "quarter")
   exindexPlot(-bmw, block = "quarter")   
   
## Extremal Index for the right and left tails 
## of the BMW log returns:
   xmpExtremes("Next: Investigate Tail Depth Dependence >")
   data(bmw)
   exindexesPlot( bmw, block = 65)
   exindexesPlot(-bmw, block = 65)