Chang Bo, Joe Harry
Department of Statistics, University of British Columbia, Vancouver, Canada.
J Appl Stat. 2019 Nov 3;47(9):1587-1615. doi: 10.1080/02664763.2019.1685080. eCollection 2020.
Vine copulas are constructed from a sequence of trees to represent dependence and conditional dependence, and a set of bivariate copulas that are applied to univariate distributions in tree 1 and to conditional univariate distributions in subsequent trees. Diagnostic methods based on measures of dependence and tail asymmetry are proposed to guide the choice of parametric bivariate copula families assigned to the edges of the trees in the vine and to assess whether a copula is constant over the conditioning value(s) for trees 2 and higher. The measures are conditional measures applied to bivariate conditional distributions in trees 2 and higher. If the diagnostic methods suggest the existence of reflection asymmetry, permutation asymmetry and possible asymmetric tail dependence, then three- or four-parameter bivariate copula families might be needed. Moreover, if the conditional dependence measures or asymmetry measures in trees 2 and up are not constant over the conditioning value(s), then non-constant copulas should be considered. We illustrate the use of the diagnostic methods for a gamma factor model and two real datasets. The examples show that better models are attained by using asymmetric and non-constant copulas under the guidance of the diagnostic tools.
藤蔓相依函数由一系列树状结构构建而成，用于表示相依性和条件相依性，以及一组二元相依函数，这些二元相依函数应用于树状结构1中的单变量分布以及后续树状结构中的条件单变量分布。提出了基于相依性度量和尾部不对称性的诊断方法，以指导分配给藤蔓中树状结构边的参数化二元相依函数族的选择，并评估相依函数在树状结构2及更高结构的条件值上是否恒定。这些度量是应用于树状结构2及更高结构中二元条件分布的条件度量。如果诊断方法表明存在反射不对称、排列不对称以及可能的不对称尾部相依性，那么可能需要三参数或四参数二元相依函数族。此外，如果树状结构2及更高结构中的条件相依性度量或不对称性度量在条件值上不恒定，那么应考虑非恒定相依函数。我们说明了诊断方法在伽马因子模型和两个真实数据集上的应用。这些例子表明，在诊断工具的指导下使用不对称和非恒定相依函数可以得到更好的模型。
