本研究介紹了一種新穎的方法，用於估計負二項時間序列數據中的改變點，採用 Copula 馬可夫鏈模型。負二項分佈在描述過度離散的計數數據方面非常有效。在本研究中，我們應用了牛頓法作為實施方法，並利用漸近正態性方法獲得區間估計。負二項時間序列具有重要的實際應用意義；然而，準確估計其改變點一直是一個具有挑戰性的問題。本研究旨在通過提出一種可行的方法來確定負二項時間序列數據中的改變點，以解決這一問題。通過本研究，我們希望為負二項時間序列中的改變點估計問題提供可靠的解決方案，並為相關領域的研究和實踐提供有價值的參考。模擬結果表明，所提出的方法在檢測變點方面表現出高度精確性，超越了傳統方法，具有顯著的優勢。最後，我們使用了2020年COVID-19大流行的死亡數據以及1851年至1962年期間英國煤礦事故中工人死亡的112年數據進行實證分析。;This study introduces a novel approach for estimating change points for negative binomial time series data, with the Copula Markov Chain model. The negative binomial distribution is highly effective in describing over-dispersed count data. In this study, we apply Newton′s method to solve the Maximum likelihood estimation (MLE) and the asymptotic normality method to obtain interval estimates. Negative binomial time series have significant practical implications; however, accurate estimation of their change points is a challenging problem. This research seeks to address this deficiency by presenting a viable approach for determining change points. Through this research, we provide a reliable solution for the change point estimation problem in negative binomial time series and offer valuable references for research and practice in the related fields. The results in the simulation studies demonstrate that the method exhibits a high level of precision in detecting change points. Finally, we use death data during the COVID-19 pandemic in 2020 and data on worker deaths from British coal mine accident over a 112-year period from 1851 to 1962 in empirical analysis for illustration.
