我們提出一套嶄新的方法論架構，用以偵測計數型時間序列資料中的結構性變化。所提方法結合了基於 Copula 的馬可夫鏈模型與零膨脹卜瓦松（ZIP）分布，並採用輪廓最大概似估計法（Profile MLE）結合牛頓–拉弗森演算法來進行模型參數的估計。在模型設計方面，我們進一步探討兩種相依結構——Clayton Copula 與 Joe Copula——在捕捉非線性序列相依性上的表現。此外，我們亦綜合考量相依強度、改變點位置、樣本大小，以及中間改變點所對應的相依參數等因素，以評估所提方法的估計準確性與穩健性。在實證分析中，我們將所提方法應用於 COVID-19 確診人數與煤礦事故數等計數資料，作為應用示範。;We propose a novel methodological framework for detecting structural changes in count time series data. The proposed method integrates the copula-based Markov chain model with the zero-inflated Poisson (ZIP) distribution and estimates model parameters using the profile maximum likelihood estimation (Profile MLE) method combined with the Newton–Raphson algorithm. In terms of model design, we further explore the performance of two dependence structures—the Clayton copula and the Joe copula—in capturing nonlinear serial dependence. Additionally, we comprehensively consider factors such as dependence strength, change-point location, sample size, and the dependence parameter associated with the intermediate change-point, in order to evaluate the accuracy and robustness for the proposed method. In the empirical analysis, we apply the proposed method to count data on confirmed COVID-19 cases and coal mining accidents for illustration.
