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研究生： 林韋成
Wei-Cheng Lin
論文名稱： Estimation in copula-based Markov mixture normal model
Estimation in copula-based Markov mixture normal model
指導教授： 孫立憲
Li-Hsien Sun
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
論文出版年： 2018
畢業學年度： 106
語文別： 英文
論文頁數： 57
中文關鍵詞： copula 、混和常態模型 、牛頓-拉弗森 、k-平均演算法 、馬可夫模型 、對數報酬
外文關鍵詞： copula, mixture normal distribution, Newton-Raphson, k-means clustering, Markov model, log return
相關次數： 點閱：27  下載：0 
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    • 在本文中，我們提出對於copula之下馬可夫鍊模型的估計問題，由於在股票市場中其厚尾的特性，我們選用混和常態模型作為我們的邊際分布，基於邊際分布為混和常態分佈和Clayton copula，我們得到相應的概似函數，為了解決最大概似估計量的問題，我們應用了牛頓-拉弗森方法，在實證分析中，我們分析了道瓊斯工業平均指數的股票價格。

    In this paper, we propose the estimation problem for a copula-based Markov model. Owing to the fat tail feature in stock market, we select mixture normal distribution as the marginal distribution for the log return. Based on the mixture normal distribution as the marginal distribution and the Clayton copula, we obtain the corresponding likelihood function. In order to solve the maximum likelihood estimators, we apply Newton Raphson method. In the empirical analysis, the stock price of Dow Jones Industrial Average is analyzed for illustration.

    Introduction 1 2 Copula-based Markov Model 3 2.1 Mixture Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Copula function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Model assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 The likelihood function of Clayton copula . . . . . . . . . . . . . . . 7 3 Method for Estimate parameters 8 3.1 Randomized Newton-Raphson Method . . . . . . . . . . . . . . . . . 8 3.2 K-means clustering algorithm . . . . . . . . . . . . . . . . . . . . . . 9 4 Simulation 13 4.1 Simulation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 5 Empirical Study 26 5.1 Data description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.2 Empirical result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 6 Conclusion 32

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