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Quadratic transformation of multivariate aggregation functions 多元聚合函数的二次变换
IF 0.7
Dependence Modeling Pub Date : 2020-01-01 DOI: 10.1515/demo-2020-0015
Prakassawat Boonmee, S. Tasena
{"title":"Quadratic transformation of multivariate aggregation functions","authors":"Prakassawat Boonmee, S. Tasena","doi":"10.1515/demo-2020-0015","DOIUrl":"https://doi.org/10.1515/demo-2020-0015","url":null,"abstract":"Abstract In this work, we prove that quadratic transformations of aggregation functions must come from quadratic aggregation functions. We also show that this is different from quadratic transformations of (multivariate) semi-copulas and quasi-copulas. In the latter case, those two classes are actually the same and consists of convex combinations of the identity map and another fixed quadratic transformation. In other words, it is a convex set with two extreme points. This result is different from the bivariate case in which the two classes are different and both are convex with four extreme points.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"8 1","pages":"254 - 261"},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2020-0015","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46578083","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}
引用次数: 1
The deFinetti representation of generalised Marshall–Olkin sequences 广义Marshall-Olkin序列的deFinetti表示
IF 0.7
Dependence Modeling Pub Date : 2020-01-01 DOI: 10.1515/demo-2020-0006
Henrik Sloot
{"title":"The deFinetti representation of generalised Marshall–Olkin sequences","authors":"Henrik Sloot","doi":"10.1515/demo-2020-0006","DOIUrl":"https://doi.org/10.1515/demo-2020-0006","url":null,"abstract":"Abstract We show that each infinite exchangeable sequence τ1, τ2, . . . of random variables of the generalised Marshall–Olkin kind can be uniquely linked to an additive subordinator via its deFinetti representation. This is useful for simulation, model estimation, and model building.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"8 1","pages":"107 - 118"},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2020-0006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46586622","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}
引用次数: 2
Bayesian estimation of generalized partition of unity copulas 单位联结广义划分的贝叶斯估计
IF 0.7
Dependence Modeling Pub Date : 2020-01-01 DOI: 10.1515/DEMO-2020-0007
A. Masuhr, M. Trede
{"title":"Bayesian estimation of generalized partition of unity copulas","authors":"A. Masuhr, M. Trede","doi":"10.1515/DEMO-2020-0007","DOIUrl":"https://doi.org/10.1515/DEMO-2020-0007","url":null,"abstract":"Abstract This paper proposes a Bayesian estimation algorithm to estimate Generalized Partition of Unity Copulas (GPUC), a class of nonparametric copulas recently introduced by [18]. The first approach is a random walk Metropolis-Hastings (RW-MH) algorithm, the second one is a random blocking random walk Metropolis-Hastings algorithm (RBRW-MH). Both approaches are Markov chain Monte Carlo methods and can cope with ˛at priors. We carry out simulation studies to determine and compare the efficiency of the algorithms. We present an empirical illustration where GPUCs are used to nonparametrically describe the dependence of exchange rate changes of the crypto-currencies Bitcoin and Ethereum.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"8 1","pages":"119 - 131"},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/DEMO-2020-0007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42283076","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}
引用次数: 3
Copula modeling for discrete random vectors 离散随机向量的Copula建模
IF 0.7
Dependence Modeling Pub Date : 2020-01-01 DOI: 10.1515/demo-2020-0022
G. Geenens
{"title":"Copula modeling for discrete random vectors","authors":"G. Geenens","doi":"10.1515/demo-2020-0022","DOIUrl":"https://doi.org/10.1515/demo-2020-0022","url":null,"abstract":"Abstract Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Sklar’s theorem, “the fundamental theorem of copulas”, makes a clear distinction between the continuous case and the discrete case, though. In particular, the copula of a discrete random vector is not fully identifiable, which causes serious inconsistencies. In spite of this, downplaying statements may be found in the related literature, where copula methods are used for modelling dependence between discrete variables. This paper calls to reconsidering the soundness of copula modelling for discrete data. It suggests a more fundamental construction which allows copula ideas to smoothly carry over to the discrete case. Actually it is an attempt at rejuvenating some century-old ideas of Udny Yule, who mentioned a similar construction a long time before copulas got in fashion.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"8 1","pages":"417 - 440"},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2020-0022","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45062337","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}
引用次数: 16
The gentleman copulist 绅士共议主义者
IF 0.7
Dependence Modeling Pub Date : 2020-01-01 DOI: 10.1515/demo-2020-0002
C. Genest, M. Scherer
{"title":"The gentleman copulist","authors":"C. Genest, M. Scherer","doi":"10.1515/demo-2020-0002","DOIUrl":"https://doi.org/10.1515/demo-2020-0002","url":null,"abstract":"Carlo Sempi is a professor in the Department of Mathematics and Physics at the Università degli Studi del Salento in Lecce, Italy. He studied mathematics at the Università degli Studi di Pavia (Laurea in Fisica, 1970) and at the University of Waterloo (Ontario, Canada), where he completed his PhD in October 1974. He then joined his current institution as professore incaricato and became professore straordinario in 2000. He was an early contributor to the theory of copulas andhas remained active to this day. He is the author or coauthor of over 125 research articles on various aspects of analysis, probabilistic metric spaces, copulas, and many related notions such as semi-copulas, quasi-copulas, anddiscrete copulas.Withhis formerPhDstudent FabrizioDurante, he also coauthored the book “Principles of Copula Theory” published by Chapman & Hall in 2015. A cosmopolitan and polyglot, he served the dependence modeling community in various ways, notably through the organization of the 2009 meeting marking the 50th anniversary of Abe Sklar’s seminal paper.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"8 1","pages":"34 - 44"},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2020-0002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43145180","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}
引用次数: 1
State dependent correlations in the Vasicek default model Vasicek默认模型中的状态相关关系
IF 0.7
Dependence Modeling Pub Date : 2020-01-01 DOI: 10.1515/demo-2020-0017
A. Metzler
{"title":"State dependent correlations in the Vasicek default model","authors":"A. Metzler","doi":"10.1515/demo-2020-0017","DOIUrl":"https://doi.org/10.1515/demo-2020-0017","url":null,"abstract":"Abstract This paper incorporates state dependent correlations (those that vary systematically with the state of the economy) into the Vasicek default model. Other approaches to randomizing correlation in the Vasicek model have either assumed that correlation is independent of the systematic risk factor (zero state dependence) or is an explicit function of the systematic risk factor (perfect state dependence). By contrast, our approach allows for an arbitrary degree of state dependence and includes both zero and perfect state dependence as special cases. This is accomplished by expressing the factor loading as a function of an auxiliary (Gaussian) variable that is correlated with the systematic risk factor. Using Federal Reserve data on delinquency rates we use maximum likelihood to estimate the parameters of the model, and find the empirical degree of state dependence to be quite high (but generally not perfect). We also find that randomizing correlation, without allowing for state dependence, does not improve the empirical performance of the Vasicek model.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"8 1","pages":"298 - 329"},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2020-0017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43756038","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}
引用次数: 0
Bayesian credibility premium with GB2 copulas GB2 copula的贝叶斯可信度溢价
IF 0.7
Dependence Modeling Pub Date : 2019-04-16 DOI: 10.2139/ssrn.3373377
Himchan Jeong, Emiliano A. Valdez
{"title":"Bayesian credibility premium with GB2 copulas","authors":"Himchan Jeong, Emiliano A. Valdez","doi":"10.2139/ssrn.3373377","DOIUrl":"https://doi.org/10.2139/ssrn.3373377","url":null,"abstract":"Abstract For observations over a period of time, Bayesian credibility premium may be used to predict the value of a response variable for a subject, given previously observed values. In this article, we formulate Bayesian credibility premium under a change of probability measure within the copula framework. Such reformulation is demonstrated using the multivariate generalized beta of the second kind (GB2) distribution. Within this family of GB2 copulas, we are able to derive explicit form of Bayesian credibility premium. Numerical illustrations show the application of these estimators in determining experience-rated insurance premium. We consider generalized Pareto as a special case.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"8 1","pages":"157 - 171"},"PeriodicalIF":0.7,"publicationDate":"2019-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84824913","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}
引用次数: 2
Volatility filtering in estimation of kurtosis (and variance) 峰度(和方差)估计中的波动滤波
IF 0.7
Dependence Modeling Pub Date : 2019-02-01 DOI: 10.1515/demo-2019-0001
Stanislav Anatolyev
{"title":"Volatility filtering in estimation of kurtosis (and variance)","authors":"Stanislav Anatolyev","doi":"10.1515/demo-2019-0001","DOIUrl":"https://doi.org/10.1515/demo-2019-0001","url":null,"abstract":"Abstract The kurtosis of the distribution of financial returns characterized by high volatility persistence and thick tails is notoriously difficult to estimate precisely. We propose a simple but effective procedure of estimating the kurtosis coefficient (and variance) based on volatility filtering that uses a simple GARCH model. In addition to an estimate, the proposed algorithm issues a signal of whether the kurtosis (or variance) is finite or infinite. We also show how to construct confidence intervals around the proposed estimates. Simulations indicate that the proposed estimates are much less median biased than the usual method-of-moments estimates, their confidence intervals having much more precise coverage probabilities. The procedure alsoworks well when the underlying volatility process is not the one the filtering technique is based on. We illustrate how the algorithm works using several actual series of returns.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"7 1","pages":"1 - 23"},"PeriodicalIF":0.7,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2019-0001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48218890","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}
引用次数: 5
Modelling cascading effects for systemic risk: Properties of the Freund copula 系统风险的级联效应建模：Freund copula的性质
IF 0.7
Dependence Modeling Pub Date : 2019-02-01 DOI: 10.1515/demo-2019-0002
S. Guzmics, G. Pflug
{"title":"Modelling cascading effects for systemic risk: Properties of the Freund copula","authors":"S. Guzmics, G. Pflug","doi":"10.1515/demo-2019-0002","DOIUrl":"https://doi.org/10.1515/demo-2019-0002","url":null,"abstract":"Abstract We consider a dependent lifetime model for systemic risk, whose basic idea was for the first time presented by Freund. This model allows to model cascading effects of defaults for arbitrarily many economic agents. We study in particular the pertaining bivariate copula function. This copula does not have a closed form and does not belong to the class of Archimedean copulas, either.We derive some monotonicity properties of it and show how to use this copula for modelling the cascade effect implicitly contained in observed CDS spreads.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"7 1","pages":"24 - 44"},"PeriodicalIF":0.7,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2019-0002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45246654","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}
引用次数: 3
Copula multivariate GARCH model with constrained Hamiltonian Monte Carlo 具有约束哈密顿量的Copula多元GARCH模型
IF 0.7
Dependence Modeling Pub Date : 2019-01-01 DOI: 10.1515/demo-2019-0006
Martin Burda, Louis Bélisle
{"title":"Copula multivariate GARCH model with constrained Hamiltonian Monte Carlo","authors":"Martin Burda, Louis Bélisle","doi":"10.1515/demo-2019-0006","DOIUrl":"https://doi.org/10.1515/demo-2019-0006","url":null,"abstract":"Abstract The Copula Multivariate GARCH (CMGARCH) model is based on a dynamic copula function with time-varying parameters. It is particularly suited for modelling dynamic dependence of non-elliptically distributed financial returns series. The model allows for capturing more flexible dependence patterns than a multivariate GARCH model and also generalizes static copula dependence models. Nonetheless, the model is subject to a number of parameter constraints that ensure positivity of variances and covariance stationarity of the modeled stochastic processes. As such, the resulting distribution of parameters of interest is highly irregular, characterized by skewness, asymmetry, and truncation, hindering the applicability and accuracy of asymptotic inference. In this paper, we propose Bayesian analysis of the CMGARCH model based on Constrained Hamiltonian Monte Carlo (CHMC), which has been shown in other contexts to yield efficient inference on complicated constrained dependence structures. In the CMGARCH context, we contrast CHMC with traditional random-walk sampling used in the previous literature and highlight the benefits of CHMC for applied researchers. We estimate the posterior mean, median and Bayesian confidence intervals for the coefficients of tail dependence. The analysis is performed in an application to a recent portfolio of S&P500 financial asset returns.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"7 1","pages":"133 - 149"},"PeriodicalIF":0.7,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2019-0006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45846307","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}
引用次数: 6
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