時空模型於台灣PM2.5資料之預測

全球各地許多的研究都發現空氣污染有害人類健康，且空氣污染問題越來越嚴重。在許多空氣汙染物中，細懸浮微粒(PM2.5)不只會危害呼吸道，還會導致其他器官的傷害。在台灣國家監測站只設立77 個，站數稀疏且設置位置不均，但空氣盒子(airbox)的設置較為密集，能收集到更多資料，做更好的預測。本篇研究使用的空氣盒子資料與Huang et al. [9](2018) 相同，且調整了他們的方法。他們的模型是採用Tzeng and Huang [16](2018) 提出的多解析度樣條基底函數(multiresolution spline basis functions) 作為解釋變數，再使用穩健迴歸(robust regression) 進行參數估計。我們在模型中增加更多基底函數與兩個氣候因子，且考慮了數個不同的時空共異函數(spatio-temporal covariance function)，不單單僅用空間共異函數(spatial covariance function)。為了比較，我們還使用最小絕對值壓縮和篩選算法(least absolute shrinkage and selection operator, Lasso) 進行估計，最後透過時空克利金法(spatio-temporal kriging)算出一步向前(one-step ahead)與兩步向前預測值(two-step ahead prediction)，利用預測表現來比較不同模型與不同估計方法。

關鍵字

空氣盒子； PM2.5 ；時空模型；多重解析度樣條基底函數；穩健迴歸；時空克利金法；最小絕對值壓縮和篩選算法

並列摘要

Many studies around the world have found the harmful effects of air pollution on human health, and the air pollution problem is becoming more serious. Among many air pollutants, suspended particulate matter (PM2.5) not only harms the respiratory system but also causes damage to other organs. In Taiwan, there are only 77 national monitoring stations which are very sparse and non-uniformly located. On the other hand, air boxes are more densely distributed. They help to collect more data for better prediction. In this research, we use the same air box data set of Huang et al. [9](2018) and modify their method. They established a spatial model based on the multiresolution spline basis functions proposed by Tzeng and Huang [16](2018) and used robust regression to estimate the parameters. We modify their model by including more basis functions and two additional climate factors. Moreover, we consider several spatio-temporal covariance functions instead of spatial covariance functions. For comparison, we also use Lasso (least absolute shrinkage and selection operator, Lasso) method to estimate the parameters. Finally, the one-step ahead and the two-step ahead predictions are computed by spatio-temporal kriging. The prediction performances by using different models and different estimators are compared.

並列關鍵字

airbox ； spatio-temporal model ； multiresolution spline basis function ； robust regression ； spatio-temporal kriging ； least absolute shrinkage and selection operator