變更點檢測是時間序列分析的重要組成部分，因為變更點的存在表明數據生成過程中發生了突然而重大的變更。檢測變更點可以幫助我們事前預警和事後分析，其被應用在許多的領域，如工業質量控制、金融市場分析、網絡流量分析等等。在傳統方法中，假設觀測值是獨立的情況下，可以使用最大概似估計器来估計變化點。然而，在許多實際應用中，觀測值通常是相依的，所以獨立假設的最大概似估計器方法通常
是低效的。在本文中，我們擴展最大概似估計器方法，將其應用在觀測值相依的情況中，我們提出一個新的變化點模型，其中序列相關遵循基於 copula 的馬爾可夫鏈模型，邊際分佈遵循常態分佈，然後我們得到其對應的概似函數，而為了解決最大概似估計量的問題，我們應用了牛頓-拉弗森方法。在實證研究中，我們分析了股票報酬數據來說明。

Change point detection is an important part of time series analysis because the existence of change points indicates that there is a sudden and significant change in the process of data generation. Detecting change points can help us with pre-warning and post analysis. It is widely used in many fields, such as industrial quality control, financial market analysis, network traffic analysis, and so on. In the literature review, the maximum likelihood estimator can be used to estimate the change point under the assumption that the observations are independent. However, in many practical applications, the observations usually have dependent structure, so the
maximum likelihood estimator method with independent hypothesis is usually inefficient. In this paper, we extend the maximum likelihood estimator method to the case of dependent observations. We propose a new change point model, which the serial correlation follows the copulabased Markov chain model, and the marginal distribution follows the normal distribution and
then obtain its corresponding likelihood function. The Newton Raphson method is applied to solve the maximum likelihood estimators. In the empirical study, we analyze the stock return data for illustration.

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