ExtremeIndexPlots {fExtremes} | R Documentation

## 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:

`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 a `times` attribute containing (in an object of class `"POSIXct"`, or an object that can be converted to that class; see `as.POSIXct`) the times/dates of each observation, then `block` may instead take the character values `"month"`, `"quarter"`, `"semester"` or `"year"`. Note, `exindexPlot` supports both numeric and character input, `exindexPlot` supports only numeric input. By default, monthly blocks or 20-day blocks are used which are thought for daily data records.
`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.

### Author(s)

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

    ## SOURCE("fExtremes.55A-ExtremeIndex")

    ## Extremal Index for the right and left tails
    ## of the BMW log returns:
       xmpExtremes("\nStart: 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("\nNext: Investigate Tail Depth Dependence >")
       data(bmw)
       exindexesPlot( bmw, block = 65)
       exindexesPlot(-bmw, block = 65)

[Package fExtremes version 221.10065 Index]