exdex-package {exdex}

exdex: Estimation of the Extremal Index

Description

The extremal index \theta is a measure of the degree of local dependence in the extremes of a stationary process. The exdex package performs frequentist inference about \theta using the methodologies proposed in Northrop (2015), Berghaus and Bucher (2018), Suveges (2007), Suveges and Davison (2010) and Holesovsky and Fusek (2020).

Details

Functions to implement four estimators of the extremal index are provided, namely

• spm: semiparametric maxima estimator, using block maxima: (Northrop, 2015; Berghaus and Bucher, 2018)

• kgaps: K-gaps estimator, using threshold inter-exceedance times (Suveges and Davison, 2010)

• dgaps: D-gaps estimator, using threshold inter-exceedance times (Holesovsky and Fusek, 2020))

• iwls: iterated weighted least squares estimator, using threshold inter-exceedance times: (Suveges, 2007)

The functions choose_b, choose_uk and choose_ud provide graphical diagnostics for choosing the respective tuning parameters of the semiparametric maxima, K-gaps and D-gaps estimators.

For the K-gaps and D-gaps models the 'exdex' package allows missing values in the data, can accommodate independent subsets of data, such as monthly or seasonal time series from different years, and can incorporate information from censored inter-exceedance times.

See vignette("exdex-vignette", package = "exdex") for an overview of the package.

Author(s)

Maintainer: Paul J. Northrop [e-mail] [copyright holder]

Authors:

• Constantinos Christodoulides [copyright holder]

References

Berghaus, B., Bucher, A. (2018) Weak convergence of a pseudo maximum likelihood estimator for the extremal index. Ann. Statist. 46(5), 2307-2335. doi:10.1214/17-AOS1621

Holesovsky, J. and Fusek, M. Estimation of the extremal index using censored distributions. Extremes 23, 197-213 (2020). doi:10.1007/s10687-020-00374-3

Northrop, P. J. (2015) An efficient semiparametric maxima estimator of the extremal index. Extremes 18(4), 585-603. doi:10.1007/s10687-015-0221-5

Suveges, M. (2007) Likelihood estimation of the extremal index. Extremes, 10, 41-55. doi:10.1007/s10687-007-0034-2

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

See Also

spm: semiparametric maxima estimator.

kgaps: K-gaps estimator.

dgaps: D-gaps estimator.

iwls: iterated weighted least squares estimator.

choose_b, choose_ud and choose_ud for choosing tuning parameters.

newlyn, sp500 and cheeseboro for example datasets.