本論文所感興趣的研究議題為PM2.5預測分析，近年來空氣汙染問題日益嚴重，PM2.5為一個重要的空氣汙染物指標，其預測尤其重要。本文以Airbox 計畫所提供的PM2.5資料集做預測分析，該資料集有著觀測站數多、觀測時間不規律和觀測誤差過大等問題，使分析極具挑戰。本文提供了一種降維分解模型來進行該資料的分析與預測，模型分為兩部分包含固定效應的平均結構與時空隨機效應，分別以降維後再投影至空間與時間的基底等方式建模，並在時空隨機效應裡加入時間的動態結構，進而藉由kalman filter輔助獲得空間與時間上的PM2.5一步或多步預測值與預測誤差。最後應用PM2.5資料集演示模型預測的結果。

In recent years, air pollution becomes a serious problem in Taiwan, in particular PM2.5 plays an important role to affect the public health. This thesis studies the topic of PM2.5 forecast. The data used in this study is from AirBox Project which collects high-frequency data from more than one thousand small measurement devices using IoT technologies. The data are available instantaneously but very irregular in time, having excessive observation errors and many missing data. This study suggests a reduced-rank decomposition model to analyze AirBox data. The model consists two parts. The mean structure of daily pattern is specified via a linear combination of products of spatial eigen-functions and temporal (hourly) eigen-functions obtained via singular value decomposition. The dependence structure is specified via the fixed rank spatial-temporal random effect model. For parameter estimation, the method of moments is used. Given the model with estimated parameters, the kalman filter is used to generate the map of the best linear spatial prediction and their prediction errors for the one-step-ahead and multi-step-ahead PM2.5 values. The methodology is demonstrated using the data at south Taiwan.

第一章 緒論 1
1.1 前言 1
1.2 文獻回顧與章節概述 2
第二章 PM2.5資料介紹與前處理 3
第三章 模型與參數估計 7
3.1 時空隨機效應模型 7
3.2 參數估計 10
3.2.1 A_μ、B_μ的估計 10
3.2.2 A 的估計 12
3.2.3 σ_ε^2、Φ、Ω_η的估計 12
第四章 預測 15
4.1 Kalman Filter 15
4.2 一步預測與多步預測 16
第五章 PM2.5資料分析 19
第六章 結論與未來展望 33
附錄 34
附錄一 PM2.5資料參數估計值 34
附錄二 簡易準則挑出的異常觀測站 47
參考文獻 49

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