多源不完整時間數列資料的處理方法比較

A Comparative Analysis for Multi-source Incomplete Time Series Data

張婉姿(wan-tzu chang)

指導教授 ： 許玉雪

國立臺北大學/商學院/統計學系/碩士(2010年)

摘要

經濟資料常見的問題是對於一研究者有興趣的時間數列資料，有多種來源，而不同來源的資料因其調查方式、調查時間和調查範圍的不同，造成資料的不一致。或是由於人為疏失或調查困難，使得所蒐集到的資料不完整，針對這種多來源且具有缺失值的時間數列資料，將其稱之為「多源不完整時間數列資料」。

本文主要是就多來源具有隨機缺失(Missing at Random，MAR)機制之時間數列資料，在狀態空間模型架構之下，藉由程式模擬，就過去研究所提出之EM演算法和馬可夫鍊-蒙地卡羅演算法(Markov Chain Monte Carlo method，MCMC)及本研究所提出之MCMC與卡門轉換(Kalman Filter)結合的MCMC-KF演算法，進行估計精確度之比較分析，並根據模擬結果以兩個來源的白肉雞價格資料進行實證分析。期望可以針對多源不完整的時間數列資料提供一個較佳的處理方法。

根據本文研究比較結果，對於多源不完整時間數列資料的實務上應用，建議研究者考慮本身之主要研究目的為何，選擇適當的處理方式。若主要目的在於整合多個來源的資料，準確找出真實母體時間數列，在充分掌握參數資訊的情況下，可考慮利用結合卡門轉換之MCMC-KF演算法；若是考慮應用上之方便性，則建議利用EM演算法，為較有效率且穩定的估計方法。

關鍵字

多源不完整時間數列 ； 狀態空間模型 ； 卡門轉換 ； EM演算法 ； MCMC演算法

並列摘要

A time series data might have multiple sources. The data collected from different sources are usually inconsistent due to different sampling design, different survey period, or estimation method. Besides, the time series data may have different type of missing. In this study, the multi-source time series data with missing values called the "Multi-source incomplete time series data."
This thesis aims to do a comparative analysis and provide proper manipulating methods for multi-source incomplete time series data. Simulation approach is used to compare EM algorithm, Markov Chain Monte Carlo method (MCMC) and MCMC with Kalman filter (MCMC-KF) under the framework of the state space model for multi-source incomplete time series data with missing under missing at random (MAR) mechanism. A practical application is conducted on the time series data of chicken prices with two sources.
The study results show that MCMC-KF has a better performance to catch the real unobserved (hidden) time series but more complicate than other algorithms. The study results suggest that for the purpose of catching the unobserved series of interest, MCMC-KF algorithm could provide accurate results with enough parameters information, while EM algorithm could provide more efficient and stable estimation.

並列關鍵字

Muti-source incomplete time series ； State-space model ； Kalman filter

參考文獻

陳金佑(2008)，「EM及MCMC演算法在多源不完整時間數列資料的比較分析」，國立臺北大學統計研究所碩士論文.

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