Online Change Point detection under a Copula-Based Markov Chain Model for Bimodal Time Series

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劉彥劭(Yan-Shao Liou) 查詢紙本館藏

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統計研究所

論文名稱

(Online Change Point detection under a Copula-Based Markov Chain Model for Bimodal Time Series)

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至系統瀏覽論文 (2025-7-31以後開放)

摘要(中)

本論文提出了貝氏在線變點檢測方法基於Clayton copula 且邊際分布為混合
常態分布的copula-Markov 模型。在模擬研究中，我們研究了相關時間序列數據
的結構變化，包括單峰數據和雙峰數據之間的轉換以及雙峰數據內部的結構變
化，並將其與邊際分布為常態分布的copula-Markov 模型進行比較，模擬的結果
指出在相關性資料由單峰改變成雙峰時，我們所使用的模型在準確率、平均絕對
誤差、真陽個數、偽陽個數皆勝過對比模型。我們應用這種方法來檢測加密貨幣
市場從2017 年到2018 年初的變點，其中包括ICO 繁榮的開始和結束，我們選用
BTC、ETH、NEO 的每日報酬率進行偵測。結果顯示了我們的方法在檢測相關時
間序列數據的變化方面的有效性，並提供了關於虛擬貨幣市場在這ICO 繁榮-蕭條
期間行為的見解。
關鍵字：在線改變點檢測，Clayton copula，馬可夫模型，貝氏推論，ICO boom

摘要(英)

In this paper, we propose an online Bayesian changepoint detection approach for dependent
time series data under the copula-based Markov model with the marginal distributions
being mixture normal distributions. Simulation studies examine structural changes in
sequential time series data with dependency, including transformation between unimodal
and bimodal data and structural changes within bimodal data. For comparison, we consider
the Clayton copula-based Markov model with normal marginal distributions as the
benchmark model. The results show that the proposed model outperforms the benchmark
model in detecting change when the correlation structure of the changes from unimodal
data to bimodal data. In the empirical analysis, we use the daily returns of BTC, ETH, and
NEO to identify change points in the cryptocurrency market from 2017 to early 2018. The
results demonstrate the effectiveness of our approach in detecting changes and providing
insight into cryptocurrency market behavior during ICO booms and busts.
Keywords: online change point detection, Clayton copula, Markov model, Bayesian
inference, ICO boom

關鍵字(中)

★ 在線改變點檢測
★ Clayton copula
★ 馬可夫模型
★ 貝氏推論
★ ICO boom

關鍵字(英)

★ online change point detection
★ Clayton copula
★ Markov model
★ Bayesian inference
★ ICO boom

論文目次

Contents
Page
Acknowledgements III
摘要IV
Abstract V
Contents VI
List of Figures VIII
List of Tables XI
Chapter 1 Introduction 1
Chapter 2 Copulas 3
2.1 Copula function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Clayton copula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.1 Clayton copula model based on the first-order Markov Chain . . . . 6
2.2.2 Mixture normal distribution . . . . . . . . . . . . . . . . . . . . . . 7
Chapter 3 Bayesian online changepoint detection 8
3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1.1 Change point conditional prior . . . . . . . . . . . . . . . . . . . . 9
3.2 Posterior predictive distribution . . . . . . . . . . . . . . . . . . . . 10
3.2.1 Changepoint algorithm based on the control model . . . . . . . . . 12
Chapter 4 Simulation 17
Chapter 5 Empirical Study 28
5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.2 Parameters setting . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Chapter 6 Conclusion 36
Appendix A — - Figures 37
References 63

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指導教授

孫立憲(Li-Hsien Sun)

審核日期

2023-7-8

推文