動態計數時間序列之估計

Abstract

本篇論文描述分析從 latent process 得到的計數資料的parameter-driven 模式之方法，且 latent process 與計數資料具有相關性。而此模型將產生十分複雜的概似函數，modified EM演算法是將 EM 演算法中的 E 步驟作了一些修改，即將 E 步驟中給定 y 的條件期望值用邊際期望值替代。我們將用兩種時間序列的例子來說明我們的方法：車流量資料和 Zeger (1988) 的小兒麻痺發生率序列。藉由架設在路邊的偵測器所收集到的資料，我們可以估計、配適及預測交通網絡中的交通狀態，而這些訊息將是信號控制以及交通車隊管理的關鍵。

This thesis describes the methodology for analyzing in parameter- driven models for time series of count data generated from latent process that characterize the correlation structure. These models result in very complex likelihoods. A modified EM algorithm is proposed which we replace the marginal expectation with the conditional expectation given y in the E step of the EM algorithm. We illustrate our method by two time series: the traffic flow data and Zeger’s polio incidence series. Through the data collected by the detectors mounted on the road, we can estimate, smooth and predict the traffic condition about the network, these information are critical to signal control and traffic queue management.