Online changepoint detection using copula-based Markov models

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黃聖翔(Sheng-Hsiang Huang) 查詢紙本館藏

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論文名稱

(Online changepoint detection using copula-based Markov models)

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摘要(中)

改變點是生成資料序列的參數突然地變化，而線上改變點偵測是當我們隨著時間得到資料的同時用來監控觀察值是否是改變點的方法。目的是為了在改變點出現之後，盡早偵測到改變點，理想的狀態之下，我們希望能在改變點出現的時間點就偵測到改變點的訊號。在這篇論文中，我們通過步長分佈去決定每個時間點最有可能的步長，並利用此步長去偵測資料變異數的改變。此外，在實務中，我們假設股價的對數報酬獨立通常是不成立的，所以我們透過 copula 之下的馬可夫鏈模型去描述股價的對數報酬之間的相關性，且我們使用的 copula 為 Clayton copula，並用常態分佈為邊際分佈。在實證分析中，S&P 500 指數為分析資料且時間點分別為 2008 金融海嘯和 2020 COVID-19 時期。

摘要(英)

A changepoint is the abrupt variation in the generative parameters of sequential data. Online changepoint detection is the method to monitor whether this observation is a changepoint as time goes on. The goal is to detect a changepoint as soon as possible after a changepoint appears, and ideally before the next observation arrives. In this paper, we focus on the
change of variance and use the most possible run length to identify changepoints. The most possible run length is determined by computing the probability of the run length distribution at each time. Furthermore, the assumption of independence for the log return of stock price data may not be realistic in practice. We propose a copula-based Markov models to describe correlation based on the Clayton copula and the marginal distribution being the normal distribution. In the empirical analysis, the S&P 500 Index during the 2008 financial crisis and the 2020 COVID-19 are analyzed for illustrations.

關鍵字(中)

★ 改變點
★ 對數報酬
★ 馬可夫鏈模型
★ 步長
★ Copula

關鍵字(英)

論文目次

Chapter 1: Introduction 1
Chapter 2: Review for the Bayesian Online Changepoint Detection 3
2.1 Model assumption and notation 3
2.2 Method for the Bayesian Online Changepoint Detection 5
Chapter 3: Copula-based Markov models 8
3.1 Copula 8
3.2 First-order Markov model with copula 10
Chapter 4: Proposed online changepoint detection method 11
4.1 Model assumption and notations 11
4.2 Proposed method for detecting changepoints 12
4.3 Selection of hyperparameters 18
Chapter 5: Simulation Study 20
5.1 Study plan for the simulation 20
5.2 Simulation results 23
5.2.1 Results for the proposed method 23
5.2.2 Results for Student’s t data 25
5.2.3 Sensitivity analysis for hyperparameters 27
5.2.4 Results for comparing with the independent method 36
5.2.5 Results for comparing with the SDAR method 41
Chapter 6: Empirical Study 45
6.1 Data description 45
6.2 Empirical results 46
Chapter 7: Conclusion 50
References 52

參考文獻

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指導教授

孫立憲

審核日期

2021-7-23

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