fit_pclik_extr_mod {ExtremalDep}

R Documentation

Fit extremal dependence models using pairwise composite likelihood

Description

Estimates the parameters of the Husler-Reiss, Extremal-$t$ and Extremal Skew-$t$ models using pairwise composite likelihood, for up to 4 dimensional datasets.

Usage

	fit_pclik_extr_mod(model, data, parastart, trace)

Arguments

model	A string with the name of the model: "hr", "Extremalt" or "Skewt".
data	A data.frame or matrix obejct with up to 4 columns.
parastart	A vector containing the initial parameter values. See Details.
trace	A non-negative integer. If positive, tracing information on the progress of the optimization is produced. See the options of the routine optim in R for details.

Details

Data must be marginally on unit Frechet scale.

If model="hr" then the vector of initial values is made of choose(d,2) positive parameters, d=2,3. If model="Extremalt" then the vector of initial values is made of choose(d,2) dependence parameters and a degree of freedom, d=2,3. If model="Skewt" then the vector of initial values is made of choose(d,2) dependence parameters, d shape (or skewness) parameters and a degree of freedom, d=2,3.

In the case of bivariate data the regular likelihood estimation is performed.

Value

Returns the vector of estimated parameters and the value of the pairwise composite log-likelihood.

Author(s)

Simone Padoan, simone.padoan@unibocconi.it, https://mypage.unibocconi.it/simonepadoan/; Boris Beranger, borisberanger@gmail.com https://www.borisberanger.com/;

References

Beranger, B. and Padoan, S. A. (2015). Extreme dependence models, chapter of the book Extreme Value Modeling and Risk Analysis: Methods and Applications, Chapman Hall/CRC.

Beranger, B., Padoan, S. A. and Sisson, S. A. (2017). Models for extremal dependence derived from skew-symmetric families. Scandinavian Journal of Statistics, 44(1), 21-45.

Examples

## Reproduce the real data analysis from
## Beranger et al. (2016), Section 5.

data(Wind)

## Vector of starting values
p0 <- c(rep(0.5,3),1)

### CLOU CLAY SALL

if (interactive()){
ext1 <- fit_pclik_extr_mod("Extremalt", CLOU.CLAY.SALL, p0, 2)
est.ext1 <- round(ext1$par,2)
p01 <- c(ext1$par[1:3],rep(0,3),ext1$par[4])
skewt1 <- fit_pclik_extr_mod("Skewt", CLOU.CLAY.SALL, p01, 2)
est.skewt1 <- round(skewt1$par,2)
}

### CLOU CLAY PAUL

if (interactive()){
ext2 <- fit_pclik_extr_mod("Extremalt", CLOU.CLAY.PAUL, p0, 2)
est.ext2 <- round(ext2$par,2)
p02 <- c(ext2$par[1:3],rep(0,3),ext2$par[4])
skewt2 <- fit_pclik_extr_mod("Skewt", CLOU.CLAY.PAUL, p02, 2)
est.skewt2 <- round(skewt2$par,2)
}

### CLAY SALL PAUL

if (interactive()){
ext3 <- fit_pclik_extr_mod("Extremalt", CLAY.SALL.PAUL, p0, 2)
est.ext3 <- round(ext3$par,2)
p03 <- c(ext3$par[1:3],rep(0,3),ext3$par[4])
skewt3 <- fit_pclik_extr_mod("Skewt", CLAY.SALL.PAUL, p03, 2)
est.skewt3 <- round(skewt3$par,2)
}

### CLAY SALL PAUL

if (interactive()){
ext4 <- fit_pclik_extr_mod("Extremalt", CLOU.SALL.PAUL, p0, 2)
est.ext4 <- round(ext4$par,2)
p04 <- c(ext4$par[1:3],rep(0,3),ext4$par[4])
skewt4 <- fit_pclik_extr_mod("Skewt", CLOU.SALL.PAUL, p04, 2)
est.skewt4 <- round(skewt4$par,2)
}

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