一种新型双参数复合扰动Copula的相关性质
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摘要
证明了双参数复合扰动Copula仍是一个Copula.给出和证明了该双参数复合扰动Copula的Kendall’sτ和Spearman’sρ的计算公式.在此基础上,讨论了两类双参数复合扰动Copula的τ和ρ谐性度量和的取值变化规律.发现这种新型双参数复合扰动Copula在拓展相关结构的形式以及拓宽和谐性度量取值范围方面都要优于单参数扰动Copula.
This paper proved that the compound perturbed Copula with two parameters was still an Copula. The formulas of Kendall's τ and Spearman's ρ for the two-parameter compound perturbed Copula were given and proved. On the basis of this,discussed the variation law of the concordance measures τ and ρ of two kinds of compound perturbed Copula with two parameters. It was found that the new two-parameter complex perturbed Copula was superior to the one-parameter perturbed Copula in extending the form of the related structure and broadening the range of the measure of concordance.
This paper proved that the compound perturbed Copula with two parameters was still an Copula. The formulas of Kendall's τ and Spearman's ρ for the two-parameter compound perturbed Copula were given and proved. On the basis of this,discussed the variation law of the concordance measures τ and ρ of two kinds of compound perturbed Copula with two parameters. It was found that the new two-parameter complex perturbed Copula was superior to the one-parameter perturbed Copula in extending the form of the related structure and broadening the range of the measure of concordance.
引文
[1]谢赤,龙瑞,曾志坚.基于时变Copula的沪深300股指期现货高频价格相依结构测度[J].系统工程,2016,34(8):24-31.
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[14] KOMORNIK J,KOMORNIKOVAM,KALICKAJ,et al. Tail dependence of enriched class of perturbed copulas with modelling applications[S]. Data Analysis&Statistical Applications,2016,53-63.
[15] NELSEN R B. An Introdution to Copulas[M]. 2nd ed. NewYork:Springer,2006.
[2] MARIUS G S,HASLIFAH M H. Estimating value-at-risk using a multivariate copula-based volatility model:Evidence from European banks. International Economics[EB/OL]. Press,corrected proof,Available online 9 March 2018.
[3] BRAHIM B,FATAH B,DJABRANE Y. Copula conditional tail expectation for multivariate financial risks[J]. Arab Journal of Mathematical Sciences,2018,24(1):82-100.
[4] GENEST C,NESLEHOVAJ,GHORBAL N B. Estimators based on Kendall's tau in multivariate copula models[J]. Australian&New Zealand Journal of Statistics,2011,53(2):157-177.
[5] COUSIN A,DI Bernardino E. On multivariate extensions of Value-at-Risk[J]. Journal of multivariate analysis,2013,119:32-46.
[6] HUTCHINSON T P,LAI C D. Continuous Bivariate Distributions,Emphasising Applications[M]. Adelaide:Rumsby Scientific Publishing,1990.
[7] SHERWOOD H,TAYLOR M D. Doubly stochastic measures with hairpin support[J]. Probab Theory Related Fields,1988,78:617-626.
[8] NELSEN R B,QUESADA M JJ,RODRIGUEZ L JA. Bivariate copulas with cubic sections[J]. J Nonparametr Statist.,1997,7:205-220.
[9] FREDRICKS G A,NELSEN R B. Copulas constructed from diagonal sections,in:V. Benes,J. Stepan(Eds.),Distributions with Given Marginals and Moment Problems[M]. Dordrecht:Kluwer Academic Publishers,1997.
[10]董永权. FGM Copula的生成与拓展[J].工程数学学报,2008,25(6):1137-1140.
[11] DURANTE F,SANCHEZ J F,FLORES M'U. Bivariate copulas generated by perturbations[J]. Fuzzy Sets and Systems,2013,228:137-144.
[12] MESIAR R,KOMORNIKOVAM,KOMORNIK J. Perturbation of bivariate copulas[J]. Fuzzy Sets and Systems,2015,268:127-140.
[13] KOMORNIK J,KOMORNIKOVAM,KALICKAJ. Dependence measures for perturbations of copulas[J]. Fuzzy Sets and Systems,2017,324:100-116.
[14] KOMORNIK J,KOMORNIKOVAM,KALICKAJ,et al. Tail dependence of enriched class of perturbed copulas with modelling applications[S]. Data Analysis&Statistical Applications,2016,53-63.
[15] NELSEN R B. An Introdution to Copulas[M]. 2nd ed. NewYork:Springer,2006.