Copula連結時間序列應用在失業率下之建模｜國立中央大學博碩士論文系統

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研究生：	吳嘉洋 Jia-Yang Wu
論文名稱：	Copula連結時間序列應用在失業率下之建模 Copula-Based Time Series with Applications to UnemploymentRates Modeling
指導教授：	鄧惠文 Huei-Wen Teng
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 統計研究所 Graduate Institute of Statistics
畢業學年度：	99
語文別：	英文
論文頁數：	57
中文關鍵詞：	GARCH 、white noise 、Archimedean copulas 、Gaussian copula
外文關鍵詞：	GARCH, white noise, Archimedean copulas, Gaussian copula
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失業率關係到一個國家的經濟而且也受到全球經濟的影響。多維時間序列也被用來處理多個國家之間的失業率。在建立多維時間序列模型的時候，我們應該考慮在每個邊際時間序列之間一個比較彈性的相關結構。近年來，copula模型在高維度的相關結構建模中提供了一個比較彈性的架構。在本篇論文中，我們考慮兩中邊際時間序列，包含white noise 和GARCH。接著，我們用不同的copula去連結這些時間序列，包括有Gaussian copula和三個比較普遍的Archimedean copulas。最後，我們透過模擬去論證我們的模型以及用台灣日本和美國的失業率去做實例分析。

The unemployment rate is related to the economics of its own country and also influenced by global economics. Multivariate time series are used for modeling unemployment rates among different countries. When modeling multivariate time series, a more flexible dependence structure among each marginal time series should be considered. Recently, the copula model provides a flexible framework for modeling high dimensional dependence structure. In this thesis, we consider two marginal time series, including the simple white
noise and the generalized autoregressive conditional heteroskedasticity (GARCH). Then, we merge these time series by a variety of copulas, including the Gaussian copula and three popular Archimedean copulas. Finally, we demonstrate our models through simulation studies and a real data analysis using unemployment rates of Taiwan, Japan, and the United States.

摘要i
Abstract ii
誌謝iii
Table of Contents iv
List of Figures vi
List of Tables viii
1 Introduction 1
2 Preliminary 3
2.1 Gaussian copulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Archimedean copulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 Clayton copulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 Frank copulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.3 Gumbel copulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.4 Independent copulas . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 Simulation studies 8
3.1 Bivariate copulas with white noise marginal time series . . . . . . . . . . . 8
3.2 Three dimensional copulas with white noise marginal time series . . . . . . 12
iv
3.3 Multivariate GARCH models linked by copulas . . . . . . . . . . . . . . . 17
4 Real data analysis 21
5 Conclusions 45
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
References 47

                                

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[9] Sklar, A. Fonctions de r´epartition `a n dimensions et leurs marges. 229–231.

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