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Selection of mixed copulas and finit...

The University of North Carolina at Charlotte.

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Selection of mixed copulas and finite mixture models with applications in finance.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Selection of mixed copulas and finite mixture models with applications in finance./
Author:	Wang, Xian.
Description:	105 p.
Notes:	Adviser: Zongwu Cai.
Contained By:	Dissertation Abstracts International69-10B.
Subject:	Statistics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3335113
ISBN:	9780549883876

Selection of mixed copulas and finite mixture models with applications in finance.
Wang, Xian.

Selection of mixed copulas and finite mixture models with applications in finance. - 105 p.

Adviser: Zongwu Cai.

Thesis (Ph.D.)--The University of North Carolina at Charlotte, 2008.

Copulas provide a powerful tool to model the dependence among variables in a more general manner than the traditional linear correlation and to capture the flexible underlying multivariate distribution. Mixed copula, which is a linear combination of copulas, is commonly used in finance and economics since it can nest different patterns of dependence structures. The work presented in this dissertation is motivated by a potential issue that many practitioners face the problem on how to choose appropriate copula functions when they apply copula method in applications. It is well known that copula theory offers modelling the joint distribution as a function of the marginal distributions plus a copula. Therefore, to estimate parameters in the model, the likelihood function can be expressed via a mixed copula form. Furthermore, to choose appropriate components in a mixed copula, we can construct the penalized likelihood function by adding an appropriate penalty function. By maximizing the penalized likelihood function, component copulas with small weights are removed by a thresholding rule provided by the given penalty function and parameters remained are estimated simultaneously.

ISBN: 9780549883876Subjects--Topical Terms:

517247
Statistics.

Selection of mixed copulas and finite mixture models with applications in finance.
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020 $a 9780549883876
035 $a (UMI)AAI3335113
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100 1 $a Wang, Xian. $3 1026753
245 1 0 $a Selection of mixed copulas and finite mixture models with applications in finance.
300 $a 105 p.
500 $a Adviser: Zongwu Cai.
500 $a Source: Dissertation Abstracts International, Volume: 69-10, Section: B, page: 6195.
502 $a Thesis (Ph.D.)--The University of North Carolina at Charlotte, 2008.
520 $a Copulas provide a powerful tool to model the dependence among variables in a more general manner than the traditional linear correlation and to capture the flexible underlying multivariate distribution. Mixed copula, which is a linear combination of copulas, is commonly used in finance and economics since it can nest different patterns of dependence structures. The work presented in this dissertation is motivated by a potential issue that many practitioners face the problem on how to choose appropriate copula functions when they apply copula method in applications. It is well known that copula theory offers modelling the joint distribution as a function of the marginal distributions plus a copula. Therefore, to estimate parameters in the model, the likelihood function can be expressed via a mixed copula form. Furthermore, to choose appropriate components in a mixed copula, we can construct the penalized likelihood function by adding an appropriate penalty function. By maximizing the penalized likelihood function, component copulas with small weights are removed by a thresholding rule provided by the given penalty function and parameters remained are estimated simultaneously.
520 $a First, I apply the proposed approach to the selection of copulas for i.i.d. random variables under the parametric setting with known marginal distributions. Furthermore, to avoid the misspecification of the marginal distributions, I propose the semiparametric copula selection model under the time series context. That is, marginal distributions are assumed to be completely unknown and can be estimated by a nonparametric method. Finally, I consider a finite mixture model which decomposes its density into the linear combination of the known density functions with unknown parameters. It can be used to characterize the distribution of the stock return which is usually non-normal. The theory derived in this dissertation allows practitioners to select a suitable mixture distribution via the penalized likelihood to model real problems.
520 $a A big challenge to establish the asymptotic theory in this dissertation is that the proposed estimator is not the exactly same as the usual maximum likelihood estimator. More specifically, when the true number of components in a mixed copula is less than that in the working model, the coefficient parameters are on the boundary of the parameter space and the dependent parameters corresponding to zero weights are in a non-identifiable subset of the parameter space. Therefore, the classical assumptions and the standard approaches can not be applied. My major contribution in this dissertation is to establish the asymptotic properties under these non-standard situations, including the rate of convergence and asymptotic normality and abnormality. In particular, I show that the limiting distribution for boundary parameters is abnormal and the penalized likelihood estimator for non-identifiable parameters converges to an arbitrary value. Moreover, to optimize penalized likelihood function, a modified EM algorithm is proposed to simplify the computation. Finally, Monte Carlo simulation studies are carried out to illustrate the finite sample performance of the proposed methods. The simulation results show that the new estimator has a high probability of selecting appropriate components under different contexts. Also, the proposed new methods are used to investigate the correlation structures and co-movements of financial stock markets.
590 $a School code: 0694.
650 4 $a Statistics. $3 517247
690 $a 0463
710 2 $a The University of North Carolina at Charlotte. $3 1026752
773 0 $t Dissertation Abstracts International $g 69-10B.
790 $a 0694
790 1 0 $a Cai, Zongwu, $e advisor
791 $a Ph.D.
792 $a 2008
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3335113