Structure learning for hierarchical Archimedean copulas

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陳彥勳(Yen-Hsun Chen) 查詢紙本館藏

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論文名稱

(Structure learning for hierarchical Archimedean copulas)

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摘要(中)

關聯結構 (copula)可以將一個多維的聯合機率函數分解為其相關聯結構與邊際分佈們的組合 ,此關聯結構為建立多維分佈模型提供了一個更加富有彈性的方式 ,其中較為常見的是可交換型的 Archimedean copulas ,他是以各個分量上相關性結構強度皆相等為假設前提下構造的 ,但在一般現實中一般很難成立 ,因此我們選擇研究分層的 Archimedean copulas (HAC) ,它是一般 Archimedean copulas的擴充 ,它允許多維分佈中各個分量間各自擁有不同的相關聯結構強度 ,使得研究非對稱型結構更為便利。在現有的 R套件軟體使用 Okhrin, Okhrin, and Schmid (2013a)提出的一個建立 HAC方法 ,由於 HAC的性質中可知道 ,任意多維分佈皆可由其邊際分佈與所有二維關聯結構所唯一決定 ,在此我們提出了另外一種新的建模的方法。為了說明我們的方法比 Okhrin, Okhrin, and Schmid (2013a)的方法較佳 ,我們利用模擬研究從6到10維的 HAC中 ,分別模擬了1000組樣本 ,並用兩種方法去反推真實模型結構 ,發現我們所提出的方法擁有較大的可能性去反推出真實的模型。在實證分析上 ,我們採用七個國家的外匯交換利率資料 (單位 :美元),時間從2010年1月1日取到 2012年3月29日 ,並利用此兩種方法去建立多維的時間序列模型。

摘要(英)

Copulas decompose a joint distribution into a dependence structure and its marginal distri¬butions, and thus provide a great deal of ﬂexibility in modelling multivariate distributions. Elliptical and exchangeable Archimedean copulas have constrained dependence structure, which however can not capture most dependence behaviour in reality. Therefore, we study the hierarchical Archimedean copula (HAC), an extension to the exchangeable Archimedean copulas, that allows more ﬂexibility for modeling non-symmetric dependence among diﬀerent variables. In contrast to a structure learning method by Okhrin and Ristig (2012) and Okhrin et al. (2013a), we propose an alternative method to construct the dependence structure of the HAC based on a fact that the structure of the copula can be uniquely recovered from all bivariate margins. In simulation studies, we show that our method produces higher correct¬ness rate to recover the correct dependence structure for an HAC compared with Okhrin and Ristig (2012). In an empirical analysis, we consider exchange rates of seven countries with a study period from 2010/1/1 to 2013/3/29, and construct a multivariate time series models.

關鍵字(中)

★ 分層阿基米德關聯性結構
★ 估計阿基米德關聯性結構
★ 相關性結構
★ 非對稱性模型結構

關鍵字(英)

★ hierarchical Archimedean copulas
★ structure learning
★ copula estimation
★ grouping parameter
★ modeling non-symmetric dependence
★ dependence structure

論文目次

Contents
摘要 i
Abstract ii
誌謝 iii
List of Figures vii
List of Tables viii
Chapter 1 Introduction 1
Chapter 2 Preliminaries 4
2.1 Backgrounds.................................... 4
2.1.1 ArchimedeanCopula ........................... 5
2.1.2 Three-dimensional hierarchical Archimedean copula . . . . . . . . . . 6
2.1.3 Higher-dimensional hierarchical Archimedean copula . . . . . . . . . 7
2.2 Samplingprocedures ............................... 7
2.3 StructureofanHAC ............................... 14
Chapter 3 Our method 17
3.1 ReviewofproceduresbyOkhrinetal.(2013a) . . . . . . . . . . . . . . . . . 17
3.2 Ourproposedmethod .............................. 18
Chapter 4 Numerical results 25
4.1 Simulationstudy ................................. 25
4.1.1 Forsixdimensionalcase ......................... 25
4.1.2 Forsevendimensionalcase ........................ 25
4.1.3 Foreightdimensionalcase ........................ 26
4.1.4 Forninedimensionalcase ........................ 27
4.1.5 Fortendimensionalcase ......................... 27
4.2 Realdataanalysis................................. 27
4.2.1 Datadescription ............................. 28
4.2.2 Dataanalysis ............................... 29
Chapter 5 Conclusions and Future works 42
5.1 Conclusions .................................... 42
5.2 Futurework .................................... 44
Reference ....................................45

參考文獻

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指導教授

鄧惠文(Huei-Wen Teng)

審核日期

2013-7-24

推文