2020/03/30 by Jan Górecki, Marius Hofert, Górecki, Jan +3
Economics, Econometrics and Finance · Mathematics · Environmental Science · #Financial Risk and Volatility Modeling #Statistical Distribution Estimation and Applications #Hydrology and Drought Analysis
paper · pdf · doi:10.48550/arxiv.2003.13301
A large number of commonly used parametric Archimedean copula (AC) families\nare restricted to a single parameter, connected to a concordance measure such\nas Kendall's tau. This often leads to poor statistical fits, particularly in\nthe joint tails, and can sometimes even limit the ability to model concordance\nor tail dependence mathematically. This work suggests outer power (OP)\ntransformations of Archimedean generators to overcome these limitations. The\ncopulas generated by OP-transformed generators can, for example, allow one to\ncapture both a given concordance measure and a tail dependence coefficient\nsimultaneously. For exchangeable OP-transformed ACs, a formula for computing\ntail dependence coefficients is obtained, as well as two feasible OP AC\nestimators are proposed and their properties studied by simulation. For\nhierarchical extensions of OP-transformed ACs, a new construction principle,\nefficient sampling and parameter estimation are addressed. By simulation,\nconvergence rate and standard errors of the proposed estimator are studied.\nExcellent tail fitting capabilities of OP-transformed hierarchical AC models\nare demonstrated in a risk management application. The results show that the OP\ntransformation is able to improve the statistical fit of exchangeable ACs,\nparticularly of those that cannot capture upper tail dependence or strong\nconcordance, as well as the statistical fit of hierarchical ACs, especially in\nterms of tail dependence and higher dimensions. Given how comparably simple it\nis to include OP transformations into existing exchangeable and hierarchical AC\nmodels, this transformation provides an attractive trade-off between\ncomputational effort and statistical improvement.\n