an:05540460
Zbl 1157.62359
Huard, David; ??vin, Guillaume; Favre, Anne-Catherine
Bayesian copula selection
EN
Comput. Stat. Data Anal. 51, No. 2, 809-822 (2006).
00247262
2006
j
62F15 62H20 62H05
copulas; model selection; Bayes' theorem; goodness-of-fit test; Kendall's tau; pseudo-likelihood
Summary: In recent years, the use of copulas has grown extremely fast and with it, the need for a simple and reliable method to choose the right copula family. Existing methods pose numerous difficulties and none is entirely satisfactory. We propose a Bayesian method to select the most probable copula family among a given set. The copula parameters are treated as nuisance variables, and hence do not have to be estimated. Furthermore, by a parameterization of the copula density in terms of Kendall's \(\tau \), the prior on the parameter is replaced by a prior on \(\tau \), conceptually more meaningful. The prior on \(\tau \), common to all families in the set of tested copulas, serves as a basis for their comparison. Using simulated data sets, we study the reliability of the method and observe the following: (1) the frequency of successful identification approaches 100\% as the sample size increases, (2) for weakly correlated variables, larger samples are necessary for reliable identification.