基於Copula 下的馬可夫鏈模型對於韋伯分佈之改變點偵測;Change point estimation for Weibull time series data with copula-based Markov chain models

Please use this identifier to cite or link to this item: https://ir.lib.ncu.edu.tw/handle/987654321/97980

Title:	基於Copula 下的馬可夫鏈模型對於韋伯分佈之改變點偵測;Change point estimation for Weibull time series data with copula-based Markov chain models
Authors:	黃伊伶;Huang, Yi-Ling
Contributors:	統計研究所
Keywords:	改變點;Copula;馬可夫鏈模型;牛頓-拉弗森方法;韋伯分佈;Change point;Copula;Markov chain;Newton-Raphson method;Weibull distribution
Date:	2025-06-23
Issue Date:	2025-10-17 12:13:32 (UTC+8)
Publisher:	國立中央大學
Abstract:	改變點偵測可以幫助識別數據結構的變化，進而反映潛在機制的轉變。而傳統的改變點偵測方法通常假設觀測值之間相互獨立，這在實務應用中往往並不成立，這可能導致使用傳統的最大概似估計法獲得準確的改變點估計存在困難。本論文研究了 Clayton copula 及 Joe copula 下的馬爾可夫鏈，其中邊際分佈是韋伯分佈，利用 copula 函數來處理序列依賴性，提供更靈活的依賴關係建模以解決非線性依賴關係。模型構建了一個新的最大概似函數，並通過牛頓-拉弗森方法來獲得改變點和模型的參數。最後，我們將該方法應用於 2020 年 COVID-19 的 VIX 數據來進行實證分析，來展示所提出方法的性能。;Change point detection is a crucial topic which identifies the structure change based on shifts in underlying mechanisms. We propose the copula-based Markov model with the Clayton copula and the Joe copula, where the marginal distribution is the Weibull distribution. The copula function is applied to deal with nonlinear dependence for sequential data. We derive the likelihood function and obtain the maximum likelihood estimation (MLE) using the Newton-Raphson method for the change points and parameters. The performance of the proposed model is illustrated through simulation studies. In empirical studies, we analyze the VIX data from the period of 2020 COVID-19 and identify the structure change by the proposed model.
Appears in Collections:	[Graduate Institute of Statistics] Electronic Thesis & Dissertation

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