Copula-based Markov chain model with binomial data

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陳韋儒(Wei-Ru Chen) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

(Copula-based Markov chain model with binomial data)

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摘要(中)

在工業和金融業中,統計過程控制（SPC）是一項重要工具，一般而言,常用SPC,例如:休哈特控製圖，位於獨立樣本下。但是，樣本可能依賴於許多工業和金融應用，標準的休哈特控製圖是不合適的。在這方面很多人應用基於copula的Markov模型在正常邊際分佈下執行SPC。在本文中，我們考慮具有二項邊際分佈的基於copula的馬爾可夫鏈模型來執行SPC。我們應用牛頓算法來獲得最大似然估計。區間估計是通過漸近理論得到的。我們還開發了獲得控制限值估計的方法，並提出了計算所提出的控製圖的平均運行長度（ARL）的模擬技術。我們使用模擬來檢查所提出的估計量的準確性。我們將我們的方法應用於韓國股市數據，並將我們的模型與二項式AR（1）進行比較。

摘要(英)

Walter Shewhart provided an important tool for statistical process control (SPC), called the Shewhart control chart (Shewhart 1931) under independent samples. However, samples may be dependent in many industrial and financial applications, and the standard Shewhart control chart is not appropriate. Long and Emura (2014) applied the copula-based Markov model to perform SPC under the normal marginal distribution. In this thesis, we consider the copula-based Markov chain model with the binomial marginal distribution to perform SPC. We apply the Newton-Raphson algorithm to obtain maximum likelihood estimates. Interval estimates are obtained by the asymptotic theory. We also develop methods to obtain the estimates of control limits and propose simulation techniques to compute the average run length (ARL) of the proposed control chart. We use simulations to check the accuracy of the proposed estimator. We apply our method to the Korean stock market data, and we compare our model with the binomial AR(1).

關鍵字(中)

★ 控製圖，Clayton copula，馬爾可夫鏈，二項式AR（1）模型

關鍵字(英)

★ control chart, Clayton copula, Markov chain, Binomial AR(1) model

論文目次

Contents
Chapter 1 Introduction…………..………………………………………………………………....1
Chapter 2 Models for serial dependent.……….……………………………………………….….2
2.1 Copula-based Markov chain model………………………………...…………….…….2
2.2 Binomial margin….……………………………………………………………3
2.3 The binomial First-order autoregressive model………………………………………5
Chapter 3 Estimation procedures…………………………………………………………9
3.1. Proposed method………………………………………………………………………...9
3.2 Other methods………………………………………………………………………….12
3.2.1 Chen and Fan’s method……………………………………………………………….12
3.2.2 Standard method……………………………………………………………………….13
3.2.3.1 Method based on binomial AR(1)…………………………………………………….14
Chapter 4 Interval estimation…….…………………………………….………………………...15
4.1 Clayton copula model…………………………………………………………….…15
4.2 Binomial AR(1) model………………….………………..…………..…………………17
Chapter 5 Average run length…………………………………………………………………….18
5.1 Definition ARL……………………………………………………………………….18
5.2 Calculation of ARL………………………………………………………………………..19
Chapter 6 Simulation…………………………………………………………………………...20
6.1. Simulation methods……………………………………………………………………..20
6.2. Simulation results for parameters…………………………………………………......21
6.3. Simulation results for ARL…….…………………………………………………......34
Chapter 7 Data Analysis………………………………………………………………………...35
Chapter 8 Conclusion and Discussion………………………………………………………...40
Appendix A…………………………………………………………………………………………42
Appendix B…………………………………………………………………………………………53
References…………………………………………………………………………………………..59

參考文獻

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指導教授

江村剛志(Takeshi Emura)

審核日期

2018-7-30

推文