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

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