本研究探討了污染型零膨脹複合卜瓦松–伽瑪（ZiCPG）過程的估計問題。此污染型 ZiCPG 模型提供了一個靈活的框架，透過將零膨脹（zero inflation）與隨機跳躍振幅（random jump sizes）同時納入具有雜訊污染的卜瓦松過程之中，用以模擬帶有跳躍之隨機過程的動態變化。然而，這也導致極大似然估計量（maximum likelihood estimator， MLE）的計算變得極具挑戰性。為了切實解決此問題，我們提出了一套基於跳躍狀態識別（jump-state identification）與粒子濾波（particle filtering）的有效程序，用以估計潛在的跳躍並緩解由雜訊污染所帶來的計算難題。此外，本研究進一步基於估計出的跳躍動態，開發出一套預測模型。在多種模擬情境下的數值結果表明，本文所提出的估計方案具有良好的表現。更重要的是，當分別應用於 PM2.5 資料集與用電量資料集時，與其他競爭模型相比，本研究所提出的預測模型在預測潛在異常上展現出更優異的性能。;This study considers the estimation problem for a contaminated zero-inflated compound Poisson–Gamma (ZiCPG) process. The contaminated ZiCPG model provides a flexible framework for modeling the dynamics of stochastic processes with jumps by simultaneously incorporating zero inflation and random jump sizes into a Poisson process with noise contamination. Consequently， computing the maximum likelihood estimator is challenging. To address this issue， we propose an effective procedure based on jump-state identification and particle filtering to estimate latent jumps and mitigate the computational challenges arising from noise contamination. A prediction model is further developed based on the estimated jumps. Numerical results from various simulation scenarios demonstrate that the proposed estimation scheme achieves satisfactory performance. Moreover， when applied separately to PM2.5 and electricity consumption datasets， the proposed prediction model demonstrates superior performance over competing methods in predicting potential anomalies.
