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研究生:莊惠菁
研究生(外文):Hui-ching Chuang
論文名稱:以狀態變換之Copula模型刻劃因時而異之相依結構
論文名稱(外文):Modelling Time-variant Dependence Structure by Regime-switching Copula Models
指導教授:管中閔管中閔引用關係陳宜廷陳宜廷引用關係
指導教授(外文):Chung-Ming KuanYi-Ting Chen
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:經濟學研究所
學門:社會及行為科學學門
學類:經濟學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:56
中文關鍵詞:馬可夫轉換coupla模型相關結構轉折點分析相依結構
外文關鍵詞:bivariate dependence structurechange-point analysisMarkov-switching copula models
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摘要
本文利用狀態變化之copula模型來刻畫因時間變化的雙變量相依結構。以馬可夫轉換(Markov switching)模型為基準,我們將copula函數之參數設定為依不同狀態而內生變化之動態模型,此模型設定適合用於刻畫雙變量相依結構的結構性轉折情形。 實證研究發現,道瓊工業股價指數與那斯達克股價指數之報酬率間的相依結構最適合利用馬可夫變換之混合常態的copula模型來描繪它們之間的相關性,亦即此二股價報酬率之間的共變性(concordant association)明顯的具有隨不同時點變換的現象。
ABSTRACTS
In this thesis, we explore the time-variant bivariate dependence structure by a class of regime switching copula models. We consider a dynamic mixed copula in which the parameters are governed by a hidden Markov chain. In our empirical study, we apply a number of MS-mixed copulae to explore bivariate dependence between the daily returns of DJIA and NASDAQ. The structural change analysis indicates that the concordant association between these two return series is time-variant. Markov switching mixed normal copula model is suitable for interpreting the bivariate dependence of DJIA and NASDAQ returns. This result implies that the dependence may switch between the low and high concordance states.
Contents
1 Introduction 1
2 Copula and dependence measures 5
2.1 Definition and Sklar''s theorem .. . 5
2.2 Concordance measures . . . 7
2.3 Tail-dependence measures . . . 8
2.4 Empirical copula and dependence measures . . . 9
2.5 Parametric copulae and their properties . . . 10
2.5.1 The normal copula . . . 10
2.5.2 The t copula. . . 11
2.5.3 The Clayton copula . . . 12
2.5.4 The Gumbel copula . . . 12
3 Markov-switching mixed copula 13
3.1 Conditional copula . . 13
3.2 MS-mixed copula. . . 15
3.2.1 The MS-normal copula . . . 16
3.2.2 The MS-Clayton copula . . . 17
3.2.3 The MS-Gumbel copula . . . 17
3.2.4 The MS-t copulae . . . 18
3.2.5 Other MS-mixed copulae . . . 19
3.3 Bivariate time series analysis . . . 20
3.4 Model estimation and evaluation . . . 21
4 Empirical Study 24
4.1 Serial dependence and univariate models. . . 24
4.2 Time-variant bivariate dependence . . . 26
4.3 The MS-mixed copulae . . . 29
5 Conclusion 32
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