PM2.5時空資料的降維分解模型與預測

Reduced-rank Decomposition on Spatial Temporal Data with Applications to PM2.5 Daily Forecasts

鍾騰逸(Teng-Yi Chung)

指導教授 ： 徐南蓉

國立清華大學/理學院/統計學研究所/碩士(2018年)

摘要

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。

關鍵字

降維分解 ； 時空資料 ； 動態結構

並列摘要

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.

並列關鍵字

Reduced-rank ； spatial and temporal data ； stata space model

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