fExtremes (version 251.70)

DataPreprocessing: Extremes Data Preprocessing

Description

A collection and description of functions for data preprocessing of extreme values. This includes tools to separate data beyond a threshold value, to compute blockwise data like block maxima, and to decluster point process data. The functions are: ll{ blockMaxima Block Maxima from a vector or a time series, findThreshold Upper threshold for a given number of extremes, pointProcess Peaks over Threshold from a vector or a time series, deCluster Declusters clustered point process data. }

Usage

blockMaxima(x, block = c("monthly", "quarterly"), doplot = FALSE)
findThreshold(x, n = floor(0.05*length(as.vector(x))), doplot = FALSE)
pointProcess(x, u = quantile(x, 0.95), doplot = FALSE)
deCluster(x, run = 20, doplot = TRUE)

Arguments

block

[blockMaxima] - 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 data

doplot

a logical value. Should the results be plotted? By default TRUE.

n

[findThreshold] - a numeric value or vector giving number of extremes above the threshold. By default, n is set to an integer representing 5% of the data from the whole data set x.

run

[deCluster] - parameter to be used in the runs method; any two consecutive threshold exceedances separated by more than this number of observations/days are considered to belong to different clusters.

u

[pointProcess] - a numeric value at which level the data are to be truncated. By default the threshold value which belongs to the 95% quantile, u=quantile(x,0.95).

x

[finThreshold][blocks][blockMaxima][deCluster] - a numeric data vector from which findThreshold and blockMaxima determine the threshold values and block maxima values. For the function deCluster<

Value

• blockMaxima returns a timeSeries object or a numeric vector of block maxima data. findThreshold returns a numeric value or vector of suitable thresholds. pointProcess returns a timeSeries object or a numeric vector of peaks over a threshold. deCluster returns a timeSeries object or a numeric vector for the declustered point process.

Details

Finding Thresholds: The function findThreshold finds a threshold so that a given number of extremes lie above. When the data are tied a threshold is found so that at least the specified number of extremes lie above. Computing Block Maxima: The function blockMaxima calculates block maxima from a vector or a time series, whereas the function blocks is more general and allows for the calculation of an arbitrary function FUN on blocks. De-Clustering Point Processes: The function deCluster declusters clustered point process data so that Poisson assumption is more tenable over a high threshold.

References

Coles S. (2001); Introduction to Statistical Modelling of Extreme Values, Springer. Embrechts, P., Klueppelberg, C., Mikosch, T. (1997); Modelling Extremal Events, Springer.

Examples

## findThreshold -
   # Threshold giving (at least) fifty exceedances for Danish data
   x = as.timeSeries(data(danishClaims))
   findThreshold(x, n = c(10, 50, 100))    
   
## blockMaxima -
   # Block Maxima (Minima) for left tail of BMW log returns:
   BMW = as.timeSeries(data(bmwRet))
   colnames(BMW) = "BMW.RET"
   head(BMW)
   x = blockMaxima( BMW, block = 65)
   head(x)
   y = blockMaxima(-BMW, block = 65)    
   head(y) 
 
## deCluster -
   # Decluster the 200 exceedances of a particular  
   # threshold in the negative BMW log-return data
   PP = pointProcess(x = -BMW, u = quantile(x, 0.75))
   PP
   dim(PP)
   DC = deCluster(x = PP, run = 15, doplot = TRUE) 
   DC
   dim(DC)