Mixture of vines for dependence modeling: Finite mixture and Cd-vine approaches with applications

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Tezin Türü: Doktora

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, İstatistik Bölümü, Türkiye

Tezin Onay Tarihi: 2018

Öğrenci: ÖMER OZAN EVKAYA

Eş Danışman: SEVTAP AYŞE KESTEL, CEYLAN YOZGATLIGİL

Özet:

Recently, there has been an increasing interest on the combination of copulas with a finite mixture model. By a finite mixture, a suitable weighted sum of a parametric densities are tied together in a probabilistic manner. The combination of vine copulas incorporated into a finite mixture model is also beneficial to capture hidden structures in a data set. On the other hand, there are limited number of studies about the mixture of vine copulas. In this dissertation, different mixture of vines are proposed for expressing the complex and hidden dependencies in a multivariate data. Firstly, the mixture of vine copulas with different dependence structures are offered to capture the complex association in higher dimension. For this reason, finite mixture of C-vine is studied with different copula pairs. Thereafter, finite mixture of C- and D-vines have been tested with the same copula family. Lastly, as a novel approach, finite number of C-vines are incorporated into a D-vine copula model to derive the association between several variables. The values of cumulative distribution functions for each component having C-vine structure are combined with D-vine by considering the temporal ordering of the components. The performance of the proposed models are tested using simulated and real data sets, then the corresponding results are interpreted in depth.