J 2021

Outer power transformations of hierarchical Archimedean copulas: Construction, sampling and estimation

GÓRECKI, Jan, Hofert MARIUS and Okhrin OSTAP

Basic information

Original name

Outer power transformations of hierarchical Archimedean copulas: Construction, sampling and estimation

Authors

GÓRECKI, Jan (203 Czech Republic, guarantor, belonging to the institution), Hofert MARIUS (124 Canada) and Okhrin OSTAP (276 Germany)

Edition

Computational Statistics & Data Analysis, 2021, 0167-9473

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

RIV identification code

RIV/47813059:19520/21:A0000251

Organization unit

School of Business Administration in Karvina

UT WoS

000609164800010

Keywords in English

Archimedean generator; Outer power transformation; Sampling; Estimation;Tail dependence coefficients; Value at risk

Tags

Změněno: 12/4/2022 13:02, Miroslava Snopková

Abstract

V originále

Outer power (OP) transformations of Archimedean generators are suggested to increase the modeling flexibility and statistical fitting capabilities of classical Archimedean copulas restricted to a single parameter. For OP-transformed Archimedean copulas, a formula for computing tail dependence coefficients is obtained, as well as two feasible OP Archimedean copula estimators are proposed and their properties studied by simulation. For hierarchical extensions of OP-transformed Archimedean copulas under the sufficient nesting condition, a new construction principle, efficient sampling and parameter estimation for models based on a single one-parameter Archimedean family are addressed. Special attention is paid to the case where the sufficient nesting condition simplifies to two types of restrictions on the corresponding parameters. By simulation, the convergence rate and standard errors of the proposed estimator are studied. Excellent tail fitting capabilities of OP-transformed hierarchical Archimedean copula models are demonstrated in a risk management application. The results show that the OP transformation is able to improve the statistical fit of exchangeable Archimedean copulas, particularly of those that cannot capture upper tail dependence or strong concordance, as well as the statistical fit of hierarchical Archimedean copulas, especially in terms of tail dependence and higher dimensions. Given how comparably simple it is to include OP transformations into existing exchangeable and hierarchical Archimedean copula models, OP transformations provide an attractive trade-off between computational effort and statistical improvement.