EM 及MCMC 演算法在多源不完整時間數列資料的應用

An Applicationof EM and MCMC for Multi-source Incomplete Time Series Data

許玉雪(Esher Hsu) ； 張婉姿(Wan-Tzu Chang) ； 陳金佑(Chin-Yu Chen)

《統計與資訊評論》 17期 (2016/09) Pp. 1-23

摘要

不同來源的時間數列資料因其抽樣設計或估計方法的不同常有不一致的現象，而此不一致的時間數列資料其缺失狀況也可能不同，如何估計此一「多源不完整時間數列資料」背後隱藏的真實時間數列資料是本文的重點。本文主要探討EM 演算法及MCMC演算法在此一「多源不完整時間數列資料」之應用，透過模擬方式，比較分析EM 演算法、MCMC-M 演算法及MCMC-KF (結合MCMC 與卡門轉換)三種演算法在處理「多源不完整時間數列資料」的表現。模擬結果顯示，對於估計「多源不完整時間數列資料」背後隱藏的真實母體數列而言，EM 演算法與本研究所提出MCMC-KF 演算法都有不錯的表現，而MCMC-KF 演算法比EM 演算法更能精確地找到潛在真實的母體數列。最後並應用兩個來源的白肉雞價格資料進行實證分析。

關鍵字

多源不完整時間數列資料 ； 缺失資料 ； 狀態空間模型 ； 卡門轉換 ； EM 演算法 ； 馬可夫蒙地卡羅法

並列摘要

A time series data could be collected from different sourceswhichare usually inconsistent andmay have different missingpatterns. This study aims to introduce an application of EM and MCMC methods for estimating the real hiddenseries of the ＂multi-source incomplete time series＂. Three methods, namely, EM, MCMC-M, and MCMC-KF (MCMC with Kalman filter) were introduced to deal withmulti-source incomplete time series. A Monte Carlo simulation was used to compare their estimation performance. The simulation results showed that both of EM and MCMC-KF methods had a good estimation performance. The study results also indicated that MCMC-KF proposed by this study had a better performance to catch the real unobserved (hidden) time series based upon the estimation precision. A practical applicationwas conducted on the time series data of chicken prices from two sources.

並列關鍵字

Multi-source incomplete time series data ； Missing data ； State-space model ； Kalman filter ； EMalgorithm ； Markov chain Monte Carlo