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。;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 change point as time goes on. The goal is to detect a changepoint as soon as possible after a change point 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.
