基於Copula 下的馬可夫鏈模型對於廣義卜瓦松分布之改變點偵測

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姓名

盧弘晉(Hung-Chin Lu) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

基於Copula 下的馬可夫鏈模型對於廣義卜瓦松分布之改變點偵測
(Change-point Estimation Based on the Copula-based Markov Chain Model for Generalized Poisson Time Series)

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至系統瀏覽論文 (2026-8-1以後開放)

摘要(中)

檢測隨時間序列數據中的轉變，稱之為改變點估計。在此篇論文當中，我們採
用廣義卜瓦松分佈（GPD）來處理計數序列數據。廣義卜瓦松分佈經常性地作為
卜瓦松分佈的改進，使其在衡量位置和離散度方面更具有靈活度。加上，我們提出
了基於copula的馬可夫鏈模型來解決數據中的非線性依賴關係。接下來利用最大似
然估計和牛頓-拉夫遜法，實現了參數和改變點估計。為了說明其有效性，我們將
該方法應用於COVID-19及礦坑事故相關數據，並隨後提供相應的實證結果進行說
明。

摘要(英)

Change-point estimation is to detect shifts in sequential data over time elapsed. We
employ the Generalized Poisson Distribution (GPD) to deal with the counting sequential
data. Occasionally, the GPD serves as a more flexible alternative to the Poisson distribution
with respect to measuring the location and dispersion. We propose a copula-based Markov
chain model to tackle the nonlinear dependence in the data. Afterwards, the parameters and
change-point estimation are achieved using profile maximum likelihood estimation, along
with the application of the Newton-Raphson method. In order to illustrate its effectiveness,
we apply the method to the data which concerned the COVID-19 pandemic and coal mining
accidents. We subsequently provide the corresponding empirical result for illustration.

關鍵字(中)

★ 改變點
★ 廣義卜瓦松分佈
★ copula

關鍵字(英)

★ Change point
★ Generalized Poisson Distribution (GPD)
★ Copula

論文目次

1 Introduction 1
2 The Proposal Model & Algorithm 3
2.1 Generalized Poisson Distribution (GPD) . . . . . . . . . . . . . . . . . . . . . 3
2.2 Copula Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.3 Change-point Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.4 Asymptotic Normal Approximation Interval . . . . . . . . . . . . . . . . . . . 9
3 Simulations 12
3.1 Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3 Generalized Poisson Distribution vs. Poisson Distribution . . . . . . . . . . . . 13
4 Empirical Study 19
5 Conclusion 23
References 24
Appendix A 26
Appendix B 28
Appendix C 55

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指導教授

孫立憲(Li-Hsien Sun)

審核日期

2024-7-26

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