Description Usage Arguments Details Value Author(s) References See Also Examples
View source: R/extremalIndex.R
Given a threshold which defines excesses above that threshold, estimate the extremal index of a dependent sequence by using the method of Ferro and Segers, 2003. The extremal index estimate can then be used to carry out automatic declustering of the sequence to identify independent clusters and estimate the GPD for cluster maxima. Graphical diagnostics of model fit are available.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  extremalIndex(y, data = NULL, threshold)
extremalIndexRangeFit(y, data = NULL, umin = quantile(y,.5), umax =
quantile(y, 0.95), nint = 10, nboot = 100, alpha = .05, estGPD=TRUE,
verbose = TRUE, trace = 10, ...)
bootExtremalIndex(x)
declust(y, r=NULL, data = NULL, ...)
## S3 method for class 'extremalIndex'
declust(y, r=NULL,...)
## S3 method for class 'declustered'
plot(x, ylab = "Data",...)
## S3 method for class 'declustered'
evm(y, data=NULL, family=gpd, ...)
## S3 method for class 'extremalIndexRangeFit'
plot(x,addNexcesses=TRUE,estGPD=TRUE,...)
## S3 method for class 'extremalIndex'
print(x,...)
## S3 method for class 'declustered'
print(x,...)
## S3 method for class 'extremalIndexRangeFit'
ggplot(data=NULL, mapping, xlab, ylab, main,
ylim = "auto",ptcol="dark blue",col="dark blue",fill="orange",
textsize=4,addNexcesses=TRUE,estGPD=TRUE,..., environment)

y 
Argument to function 
data 
A data frame containing 
threshold 
The threshold for 
family 
The type of extreme value model. The user should not change
this from its default in 
x 
Objects passed to methods. 
r 
Positivie integer: run length to be used under "runs" declustering. If specified then socalled "runs" declustering will be carried out, otherwise defaults to NULL in which case the automatic "intervals" declustering method of Ferro and Segers is used. 
umin 
The minimum threshold above which to esimate the parameters. 
umax 
The maximum threshold above which to esimate the parameters. 
nint 
The number of thresholds at which to perform the estimation. 
nboot 
Number of bootstrap samples to simulate at each threshold for estimation. 
alpha 
100(1  alpha)% confidence intervals will be plotted with the
point estimates. Defaults to 
xlab 
Label for the xaxis (ggplot). 
ylab 
Label for the yaxis (ggplot). 
addNexcesses 
Whether to annotate the top axis of plots with the
number of excesses above the corresponding threhsold. Defaults to

estGPD 
Whether to estimate GPD parameters at each choice of
thereshold – defaults to 
verbose 
Whether to report on progress in RangeFit calculations.
Defaults to 
trace 
How frequently to report bootstrap progress in RangeFit calculations. Defaults to 10. 
mapping, main, ylim, ptcol, col, fill, textsize, environment 
Further arguments to ggplot method. 
... 
Further arguments to methods. 
The function extremalIndex
estimates the extremal index of a
dependent series of observations above a given threshold threshold
,
returning an object of class "extremalIndex". Plot and print methods are
available for this class. A graphical diagnostic akin to Figure 1 in Ferro
and Segers (2003) is produced by the plot
method for this class.
This plot is used to test the model assumption underpinning the estimation,
with good fit being indicated by interexceedance times which correspond to
intercluster times lying close to the diagonal line indicated.
In addition to good model fit, an appropriate choice of threshold is one
above which the estimated extremal index is stable over further, higher
thresholds (up to estimation uncertainty). This can be assessed by using
the function extremalIndexRangeFit
, which examines a range of
threshold values. At each threshold, the extremal index is estimated; that
estimate is used to decluster the series and the parameters of the GPD are
optionally estimated for the resulting declustered series. Uncertainty in
the estimation of the extremal index and GPD parameters is assessed by using
a bootstrap scheme which accounts for uncertainty in the extremal index
estimation, and the corresponding uncertainty in the declustering of the
series. There are plot
and ggplot
methods for output of this function, which is of class extremalIndexRangeFit
.
The function declust
returns an object of class "declustered",
identifying independent clusters in the original series. Print, plot and
show methods are available for this class. The GPD model can be fitted to
objects of this class, including the use of covariates in the linear
predictors for the parameters of the GPD. See examples below.
The function extremalIndex
returns a list of class
"extremalIndex":
EIintervals 
Estimate of the extremal index by using the intervals estimator of Ferro and Segers. 
threshold 
threshold for declustering and estimation 
TotalN 
length of original data series 
nExceed 
number of exceedances of 
thExceedanceProb 
probablity of threshold exceedance in original series. 
call 
the original function call 
interExceedTimes 
times between threshold exceedances 
thExceedances 
observation from the original series which are above

exceedanceTimes 
times of occurrance of threshold exceedances 
y 
original dependent series 
data 
data frame or NULL 
The function declust
returns a list of type "declustered":
clusters 
integer labels assigning threshold exceedances to clusters 
sizes 
number of exceedances in each cluster 
clusterMaxima 
vector made up of the largest observation from each distinct cluster. In the case of ties, the first value is taken. 
isClusterMax 
logical; length equal to number of threshold
exceedances, value is 
y 
see entry for object of class "extremalIndex" above 
data 
see entry for object of class "extremalIndex" above 
threshold 
see entry for object of class "extremalIndex" above 
EIintervals 
see entry for object of class "extremalIndex" above 
call 
see entry for object of class "extremalIndex" above 
InterExceedTimes 
times between threshold exceedances, length is one less than the number of threshold exceedances 
InterCluster 
logical:
indicates inter exceedance times larger than 
thExceedances 
see entry for object of class "extremalIndex" above 
exceedanceTimes 
see entry for object of class "extremalIndex" above 
r 
run length used for declustering 
nClusters 
Number of indenendent clusters identified 
method 
Method used for declustering (either "intervals" or "runs") 
The function bootExtremalIndex
return a single vector corersponding
to a bootstrap sample from the original series: observations are censored at
threshold
so that values below this threshold are indicated by the
value 1.
The method evm
for class "declustered" returns an object of type
"evmOpt" or "evmSim" depending on the precise function call  see
documentation for evm
.
Janet E. Heffernan
Ferro, C.A.T. and Segers, J., (2003) "Inference for clusters of Extreme Values", JRSS B 65, Part 2, pp 545–556.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27  par(mfrow=c(2,2));
extremalIndexRangeFit(summer$O3,nboot=10)
ei < extremalIndex(summer$O3,threshold=45)
plot(ei)
d < declust(ei)
plot(d)
evm(d)
## fitting with covariates:
so2 < extremalIndex(SO2,data=winter,threshold=15)
plot(so2)
so2 < extremalIndex(SO2,data=winter,threshold=20)
plot(so2) ## fits better
so2.d < declust(so2)
par(mfrow=c(1,1)); plot(so2.d)
so2.d.gpd < evm(so2.d) # AIC 661.1
evm(so2.d,phi=~NO)
evm(so2.d,phi=~NO2)
evm(so2.d,phi=~O3) # better AIC 651.9
evm(so2.d,phi=~PM10)
so2.d.gpd.o3 < evm(so2.d,phi=~O3)
par(mfrow=c(2,2)); plot(so2.d.gpd.o3)

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