Abstract Copulas C C for which (CtC)2=CtC {({C}^{t}C)}^{2}={C}^{t}C are called pre-idempotent copulas, of which well-studied examples are idempotent copulas and complete dependence copulas. As such, we shall work mainly with the topology induced by the modified Sobolev norm, with respect to which the class ℛ {mathcal{ {mathcal R} }} of pre-idempotent copulas is closed and the class of factorizable copulas is a dense subset of ℛ {mathcal{ {mathcal R} }} . Identifying copulas with Markov operators on L2 {L}^{2} , the one-to-one correspondence between pre-idempotent copulas and partial isometries is one of our main tools. In the same spirit as Darsow and Olsen’s work on idempotent copulas, we obtain an explicit characterization of pre-idempotent copulas, which is split into cases according to the atomicity of its associated σ sigma -algebras, where the nonatomic case gives all factorizable copulas and the totally atomic case yields conjugates of ordinal sums of copies of the product copula.
摘要(C - t - C) 2 = C - t - C {({C}^{t}C)}^{2}={C}^{t}C的copulc - C被称为前幂等偶，其中研究较多的例子是幂等偶和完全相关copulc。因此，我们将主要研究由修正Sobolev范数引起的拓扑结构，在该拓扑结构下，前幂等copulas的类群∑{mathcal{{mathcal R}}}是封闭的，而可分解copulas的类群是∑{mathcal{{mathcal R}}}的密集子集。用l2 {L}^{2}上的马尔可夫算子识别联结，前幂等联结与部分等距的一一对应是我们的主要工具之一。与Darsow和Olsen关于幂等幂偶的研究精神相同，我们得到了前幂等幂偶的显式刻画，根据其相关σ σ -代数的原子性将其分成若干种情况，其中非原子情况给出了所有可分解的幂等幂偶，而全原子情况给出了乘积幂等幂偶的序和的共轭。
{"title":"Characterization of pre-idempotent Copulas","authors":"Wongtawan Chamnan, Songkiat Sumetkijakan","doi":"10.1515/demo-2023-0106","DOIUrl":"https://doi.org/10.1515/demo-2023-0106","url":null,"abstract":"Abstract Copulas <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>C</m:mi> </m:math> C for which <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:msup> <m:mrow> <m:mi>C</m:mi> </m:mrow> <m:mrow> <m:mi>t</m:mi> </m:mrow> </m:msup> <m:mi>C</m:mi> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:mo>=</m:mo> <m:msup> <m:mrow> <m:mi>C</m:mi> </m:mrow> <m:mrow> <m:mi>t</m:mi> </m:mrow> </m:msup> <m:mi>C</m:mi> </m:math> {({C}^{t}C)}^{2}={C}^{t}C are called pre-idempotent copulas, of which well-studied examples are idempotent copulas and complete dependence copulas. As such, we shall work mainly with the topology induced by the modified Sobolev norm, with respect to which the class <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">ℛ</m:mi> </m:math> {mathcal{ {mathcal R} }} of pre-idempotent copulas is closed and the class of factorizable copulas is a dense subset of <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">ℛ</m:mi> </m:math> {mathcal{ {mathcal R} }} . Identifying copulas with Markov operators on <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mi>L</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> </m:math> {L}^{2} , the one-to-one correspondence between pre-idempotent copulas and partial isometries is one of our main tools. In the same spirit as Darsow and Olsen’s work on idempotent copulas, we obtain an explicit characterization of pre-idempotent copulas, which is split into cases according to the atomicity of its associated <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>σ</m:mi> </m:math> sigma -algebras, where the nonatomic case gives all factorizable copulas and the totally atomic case yields conjugates of ordinal sums of copies of the product copula.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135661990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"When copulas and smoothing met: An interview with Irène Gijbels","authors":"C. Genest, M. Scherer","doi":"10.1515/demo-2022-0154","DOIUrl":"https://doi.org/10.1515/demo-2022-0154","url":null,"abstract":"","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49362457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Acyclic phase-type (PH) distributions have been a popular tool in survival analysis, thanks to their natural interpretation in terms of aging toward its inevitable absorption. In this article, we consider an extension to the bivariate setting for the modeling of joint lifetimes. In contrast to previous models in the literature that were based on a separate estimation of the marginal behavior and the dependence structure through a copula, we propose a new time-inhomogeneous version of a multivariate PH (mIPH) class that leads to a model for joint lifetimes without that separation. We study properties of mIPH class members and provide an adapted estimation procedure that allows for right-censoring and covariate information. We show that initial distribution vectors in our construction can be tailored to reflect the dependence of the random variables and use multinomial regression to determine the influence of covariates on starting probabilities. Moreover, we highlight the flexibility and parsimony, in terms of needed phases, introduced by the time inhomogeneity. Numerical illustrations are given for the data set of joint lifetimes of Frees et al., where 10 phases turn out to be sufficient for a reasonable fitting performance. As a by-product, the proposed approach enables a natural causal interpretation of the association in the aging mechanism of joint lifetimes that goes beyond a statistical fit.
{"title":"Joint lifetime modeling with matrix distributions","authors":"H. Albrecher, Martin Bladt, Alaric J. A. Müller","doi":"10.1515/demo-2022-0153","DOIUrl":"https://doi.org/10.1515/demo-2022-0153","url":null,"abstract":"Abstract Acyclic phase-type (PH) distributions have been a popular tool in survival analysis, thanks to their natural interpretation in terms of aging toward its inevitable absorption. In this article, we consider an extension to the bivariate setting for the modeling of joint lifetimes. In contrast to previous models in the literature that were based on a separate estimation of the marginal behavior and the dependence structure through a copula, we propose a new time-inhomogeneous version of a multivariate PH (mIPH) class that leads to a model for joint lifetimes without that separation. We study properties of mIPH class members and provide an adapted estimation procedure that allows for right-censoring and covariate information. We show that initial distribution vectors in our construction can be tailored to reflect the dependence of the random variables and use multinomial regression to determine the influence of covariates on starting probabilities. Moreover, we highlight the flexibility and parsimony, in terms of needed phases, introduced by the time inhomogeneity. Numerical illustrations are given for the data set of joint lifetimes of Frees et al., where 10 phases turn out to be sufficient for a reasonable fitting performance. As a by-product, the proposed approach enables a natural causal interpretation of the association in the aging mechanism of joint lifetimes that goes beyond a statistical fit.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45079171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Juan José Fernández-Durán, María Mercedes Gregorio-Domínguez
Abstract The probability integral transform of a continuous random variable X X with distribution function FX {F}_{X} is a uniformly distributed random variable U=FX(X) U={F}_{X}left(X) . We define the angular probability integral transform (APIT) as θU=2πU=2πFX(X) {theta }_{U}=2pi U=2pi {F}_{X}left(X) , which corresponds to a uniformly distributed angle on the unit circle. For circular (angular) random variables, the sum modulus 2 π pi of absolutely continuous independent circular uniform random variables is a circular uniform random variable, that is, the circular uniform distribution is closed under summation modulus 2 π pi , and it is a stable continuous distribution on the unit circle. If we consider the sum (difference) of the APITs of two random variables, X1 {X}_{1} and X2 {X}_{2} , and test for the circular uniformity of their sum (difference) modulus 2 π pi , this is equivalent to test of independence of the original variables. In this study, we used a flexible family of nonnegative trigonometric sums (NNTS) circular distributions, which include the uniform circular distribution as a member of the family, to evaluate the power of the proposed independence test by generating samples from NNTS alternative distributions that could be at a closer proximity with respect to the circular uniform null distribution.
连续随机变量X X对分布函数F X {F＿X}的概率积分变换是均匀分布随机变量U=F X (X) U={F＿X}{}{}left (X)。我们定义角概率积分变换(APIT)为θ U=2 π U=2 π F X (X) {theta ＿U}=2{}pi U=2 pi F＿X{}{}left (X)，它对应于单位圆上的均匀分布角。对于圆(角)随机变量，绝对连续独立圆形均匀随机变量的和模2 π pi为圆形均匀随机变量，即圆形均匀分布在和模2 π pi下闭合，在单位圆上为稳定连续分布。如果我们考虑两个随机变量x1 X＿1和x2 {X＿2}的APITs的和(差)，并检验它们的和(差)模2 π {}{}{}pi的圆形均匀性，这相当于检验原始变量的独立性。在这项研究中，我们使用了一个灵活的非负三角和(NNTS)圆形分布族，其中包括均匀圆形分布作为该家族的成员，通过从NNTS替代分布中生成样本来评估所提出的独立性检验的能力，这些分布可能更接近于圆形均匀零分布。
{"title":"Test of bivariate independence based on angular probability integral transform with emphasis on circular-circular and circular-linear data","authors":"Juan José Fernández-Durán, María Mercedes Gregorio-Domínguez","doi":"10.1515/demo-2023-0103","DOIUrl":"https://doi.org/10.1515/demo-2023-0103","url":null,"abstract":"Abstract The probability integral transform of a continuous random variable <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>X</m:mi> </m:math> X with distribution function <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi>F</m:mi> </m:mrow> <m:mrow> <m:mi>X</m:mi> </m:mrow> </m:msub> </m:math> {F}_{X} is a uniformly distributed random variable <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>U</m:mi> <m:mo>=</m:mo> <m:msub> <m:mrow> <m:mi>F</m:mi> </m:mrow> <m:mrow> <m:mi>X</m:mi> </m:mrow> </m:msub> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>X</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> U={F}_{X}left(X) . We define the angular probability integral transform (APIT) as <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi>θ</m:mi> </m:mrow> <m:mrow> <m:mi>U</m:mi> </m:mrow> </m:msub> <m:mo>=</m:mo> <m:mn>2</m:mn> <m:mi>π</m:mi> <m:mi>U</m:mi> <m:mo>=</m:mo> <m:mn>2</m:mn> <m:mi>π</m:mi> <m:msub> <m:mrow> <m:mi>F</m:mi> </m:mrow> <m:mrow> <m:mi>X</m:mi> </m:mrow> </m:msub> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>X</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {theta }_{U}=2pi U=2pi {F}_{X}left(X) , which corresponds to a uniformly distributed angle on the unit circle. For circular (angular) random variables, the sum modulus 2 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>π</m:mi> </m:math> pi of absolutely continuous independent circular uniform random variables is a circular uniform random variable, that is, the circular uniform distribution is closed under summation modulus 2 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>π</m:mi> </m:math> pi , and it is a stable continuous distribution on the unit circle. If we consider the sum (difference) of the APITs of two random variables, <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi>X</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> </m:math> {X}_{1} and <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi>X</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> </m:math> {X}_{2} , and test for the circular uniformity of their sum (difference) modulus 2 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>π</m:mi> </m:math> pi , this is equivalent to test of independence of the original variables. In this study, we used a flexible family of nonnegative trigonometric sums (NNTS) circular distributions, which include the uniform circular distribution as a member of the family, to evaluate the power of the proposed independence test by generating samples from NNTS alternative distributions that could be at a closer proximity with respect to the circular uniform null distribution.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135059226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This review discusses methods of testing for explosive bubbles in time series. A large number of recently developed testing methods under various assumptions about innovation of errors are covered. The review also considers the methods for dating explosive (bubble) regimes. Special attention is devoted to time-varying volatility in the errors. Moreover, the modelling of possible relationships between time series with explosive regimes is discussed.
{"title":"Testing for explosive bubbles: a review","authors":"Anton Skrobotov","doi":"10.1515/demo-2022-0152","DOIUrl":"https://doi.org/10.1515/demo-2022-0152","url":null,"abstract":"Abstract This review discusses methods of testing for explosive bubbles in time series. A large number of recently developed testing methods under various assumptions about innovation of errors are covered. The review also considers the methods for dating explosive (bubble) regimes. Special attention is devoted to time-varying volatility in the errors. Moreover, the modelling of possible relationships between time series with explosive regimes is discussed.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135126904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Functions f f on [0,1]m {left[0,1]}^{m} such that every composition f∘(g1,…,gm) fcirc left({g}_{1},ldots ,{g}_{m}) with d d -dimensional distribution functions g1,…,gm {g}_{1},ldots ,{g}_{m} is again a distribution function, turn out to be characterized by a very natural monotonicity condition, which for d=2 d=2 means ultramodularity. For m=1 m=1 (and d=2 d=2 ), this is equivalent with increasing convexity.
函数f f on [0,1] m {left[0,1]}^{m}使得fcirc left({g}_{1}，ldots，{g}_{m})与d维分布函数g 1，…，g m {g}_{1}，ldots，{g}_{m}的每一个组合都是一个分布函数，证明它具有一个非常自然的单调性条件，对于d=2, d=2意味着超模性。对于m=1 m=1(和d=2 d=2)，这等同于增加凸性。
{"title":"Functions operating on several multivariate distribution functions","authors":"Paul Ressel","doi":"10.1515/demo-2023-0104","DOIUrl":"https://doi.org/10.1515/demo-2023-0104","url":null,"abstract":"Abstract Functions <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>f</m:mi> </m:math> f on <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mrow> <m:mo>[</m:mo> <m:mrow> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mn>1</m:mn> </m:mrow> <m:mo>]</m:mo> </m:mrow> </m:mrow> <m:mrow> <m:mi>m</m:mi> </m:mrow> </m:msup> </m:math> {left[0,1]}^{m} such that every composition <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>f</m:mi> <m:mrow> <m:mo>∘</m:mo> </m:mrow> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi>g</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>,</m:mo> <m:mrow> <m:mo>…</m:mo> </m:mrow> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi>g</m:mi> </m:mrow> <m:mrow> <m:mi>m</m:mi> </m:mrow> </m:msub> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> fcirc left({g}_{1},ldots ,{g}_{m}) with <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>d</m:mi> </m:math> d -dimensional distribution functions <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi>g</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo form=\"prefix\">,</m:mo> <m:mrow> <m:mo>…</m:mo> </m:mrow> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi>g</m:mi> </m:mrow> <m:mrow> <m:mi>m</m:mi> </m:mrow> </m:msub> </m:math> {g}_{1},ldots ,{g}_{m} is again a distribution function, turn out to be characterized by a very natural monotonicity condition, which for <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>d</m:mi> <m:mo>=</m:mo> <m:mn>2</m:mn> </m:math> d=2 means ultramodularity. For <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>m</m:mi> <m:mo>=</m:mo> <m:mn>1</m:mn> </m:math> m=1 (and <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>d</m:mi> <m:mo>=</m:mo> <m:mn>2</m:mn> </m:math> d=2 ), this is equivalent with increasing convexity.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135007458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Working with shuffles, we establish a close link between Kendall’s τ tau , the so-called length measure, and the surface area of bivariate copulas and derive some consequences. While it is well known that Spearman’s ρ rho of a bivariate copula A A is a rescaled version of the volume of the area under the graph of A A , in this contribution we show that the other famous concordance measure, Kendall’s τ tau , allows for a simple geometric interpretation as well – it is inextricably linked to the surface area of A A .
{"title":"A link between Kendall’s <i>τ</i>, the length measure and the surface of bivariate copulas, and a consequence to copulas with self-similar support","authors":"Juan Fernández Sánchez, Wolfgang Trutschnig","doi":"10.1515/demo-2023-0105","DOIUrl":"https://doi.org/10.1515/demo-2023-0105","url":null,"abstract":"Abstract Working with shuffles, we establish a close link between Kendall’s <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>τ</m:mi> </m:math> tau , the so-called length measure, and the surface area of bivariate copulas and derive some consequences. While it is well known that Spearman’s <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>ρ</m:mi> </m:math> rho of a bivariate copula <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>A</m:mi> </m:math> A is a rescaled version of the volume of the area under the graph of <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>A</m:mi> </m:math> A , in this contribution we show that the other famous concordance measure, Kendall’s <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>τ</m:mi> </m:math> tau , allows for a simple geometric interpretation as well – it is inextricably linked to the surface area of <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>A</m:mi> </m:math> A .","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135604265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A family of bivariate copulas given by: for v + 2 u < 2 v+2ult 2 , C ( u , v ) = F ( 2 F − 1 ( v ∕ 2 ) + F − 1 ( u ) ) Cleft(u,v)=Fleft(2{F}^{-1}left(v/2)+{F}^{-1}left(u)) , where F F is a strictly increasing cumulative distribution function of a symmetric, continuous random variable, and for v + 2 u ≥ 2 v+2uge 2 , C ( u , v ) = u + v − 1 Cleft(u,v)=u+v-1 , is introduced. The basic properties and necessary conditions for absolute continuity of C C are discussed. Several examples are provided.
{"title":"On copulas with a trapezoid support","authors":"P. Jaworski","doi":"10.1515/demo-2023-0101","DOIUrl":"https://doi.org/10.1515/demo-2023-0101","url":null,"abstract":"Abstract A family of bivariate copulas given by: for v + 2 u < 2 v+2ult 2 , C ( u , v ) = F ( 2 F − 1 ( v ∕ 2 ) + F − 1 ( u ) ) Cleft(u,v)=Fleft(2{F}^{-1}left(v/2)+{F}^{-1}left(u)) , where F F is a strictly increasing cumulative distribution function of a symmetric, continuous random variable, and for v + 2 u ≥ 2 v+2uge 2 , C ( u , v ) = u + v − 1 Cleft(u,v)=u+v-1 , is introduced. The basic properties and necessary conditions for absolute continuity of C C are discussed. Several examples are provided.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46671910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This article proposes a framework to model the mutual volatility transmission between multiple assets and multiple trading places in different time zones. The model is estimated using a dataset containing daily returns of three stock indices – the MSCI Japan, the EuroStoxx 50, and the S&P 500 – each traded at three major trading places: the stock exchanges in Tokyo, London, and New York. Strong volatility transmission effects can be observed between New York and Tokyo, whereas current volatility in New York mostly depends on past volatility in New York. For the assets in consideration, spillovers are strong across trading zones, but weak across assets, suggesting a close connection between market places but only a loose volatility link between international stock indices. Volatility impulse response functions indicate a long-lasting and comparably large response of volatility in Tokyo, whereas they suggest a quicker volatility decay in London and New York.
{"title":"Mutual volatility transmission between assets and trading places","authors":"Andreas Masuhr, Mark Trede","doi":"10.1515/demo-2022-0155","DOIUrl":"https://doi.org/10.1515/demo-2022-0155","url":null,"abstract":"Abstract This article proposes a framework to model the mutual volatility transmission between multiple assets and multiple trading places in different time zones. The model is estimated using a dataset containing daily returns of three stock indices – the MSCI Japan, the EuroStoxx 50, and the S&P 500 – each traded at three major trading places: the stock exchanges in Tokyo, London, and New York. Strong volatility transmission effects can be observed between New York and Tokyo, whereas current volatility in New York mostly depends on past volatility in New York. For the assets in consideration, spillovers are strong across trading zones, but weak across assets, suggesting a close connection between market places but only a loose volatility link between international stock indices. Volatility impulse response functions indicate a long-lasting and comparably large response of volatility in Tokyo, whereas they suggest a quicker volatility decay in London and New York.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135006813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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