exdex (version 1.0.1)

choose_uk: Threshold \(u\) and runs parameter \(K\) diagnostic for the \(K\)-gaps estimator

Description

Creates data for a plot to aid the choice of the threshold and run parameter \(K\) for the \(K\)-gaps estimator (see kgaps). plot.choose_uk creates the plot.

Usage

choose_uk(data, u, k = 1)

Arguments

data

A numeric vector of raw data. No missing values are allowed.

u, k

Numeric vectors. u is a vector of extreme value thresholds applied to data. k is a vector of values of the run parameter \(K\), as defined in Suveges and Davison (2010). See kgaps for more details.

Value

An object (a list) of class c("choose_uk", "exdex") containing

imt

an object of class c("kgaps_imt", "exdex") returned from kgaps_imt.

theta

a length(u) by length(k) matrix. Element (i,j) of theta contains an object (a list) of class c("kgaps", "exdex"), a result of a call kgaps(data, u[j], k[i]) to kgaps.

Details

For each combination of threshold in u and \(K\) in k the functions kgaps and kgaps_imt are called in order to estimate \(\theta\) and to perform the information matrix test of Suveges and Davison (2010).

References

Suveges, M. and Davison, A. C. (2010) Model misspecification in peaks over threshold analysis, The Annals of Applied Statistics, 4(1), 203-221. https://doi.org/10.1214/09-AOAS292

See Also

kgaps for maximum likelihood estimation of the extremal index \(\theta\) using the \(K\)-gaps model.

kgaps_imt for the information matrix test under the \(K\)-gaps model

plot.choose_uk to produce the diagnostic plot.

Examples

# NOT RUN {
### S&P 500 index

# Multiple thresholds and run parameters
u <- quantile(sp500, probs = seq(0.1, 0.9, by = 0.1))
imt_theta <- choose_uk(sp500, u = u, k = 1:5)
plot(imt_theta)
plot(imt_theta, uprob = TRUE)
plot(imt_theta, y = "theta")

# One run parameter K, many thresholds u
u <- quantile(sp500, probs = seq(0.1, 0.9, by = 0.1))
imt_theta <- choose_uk(sp500, u = u, k = 1)
plot(imt_theta)
plot(imt_theta, y = "theta")

# One threshold u, many run parameters K
u <- quantile(sp500, probs = 0.9)
imt_theta <- choose_uk(sp500, u = u, k = 1:5)
plot(imt_theta)
plot(imt_theta, y = "theta")

### Newlyn sea surges

u <- quantile(newlyn, probs = seq(0.1, 0.9, by = 0.1))
imt_theta <- choose_uk(newlyn, u = u, k = 1:5)
plot(imt_theta, uprob = TRUE)
# }