近年空氣品質的議題十分受到注目，其資料往往個具有時間與空間的性質，分析方法從傳統的時間序列、空間統計，到近期相互結合的時空模型。在Shuvo Bakar et al.(2011)提出Modified AR model(MAR)而Gelfand et al.(2005) 提出 Dynamic spatio-temporal model(DYN) 皆利用了時間序列，均是其空間變異具有時間自我相關，當作其時空效果，因此本文將比較其兩者，在比較中可發現，在DYN 其共變量效果與空間變異隨時間而改變，因此兩點觀測樣本之相關性與共變量效果變異有其相關，之後對各種不同情況的下模擬，並進行配適及預測能力進行對比，在模擬結果可得知在共變量不變時，即主要趨勢不變時，MAR 明顯優於 DYN，反之亦然。而在共變量效果不變下，空間變異改變時，DYN 其模型配適明顯估計較好，但由於其較複雜，導致其變異較大。最後進行了真實資料分析，在我們所使用的第一筆資料發現其共變量效果有明顯改變，與模擬結果一致，DYN 優於 MAR，而第二筆資料中發現其共變量效果有改變，但其個別時間的的平均共變量效果解釋相對整體共變量效果解釋，因此在此時使用 MAR 相對較好。

The issue of air quality has attracted much attention recently. The related data to study air quality intrinsically have complex spatial and temporal structures. Conventional analysis approaches are spatio-temporal statistics. In this article, we investigate the properties of two models, modified AR model (Shuvo Bakar et al., 2011) and dynamic spatio-temporal model (DYN, Gelfand et al., 2005). There are many important differences in trend effect and space-time correlation structures.
Simulation studies are conducted to compare the performance of two models in terms of predictive accuracy and model fitting criteria. We simulated data sets with different trend effect and space-time correlation structures and used Markov chain Monte Carlo (MCMC) techniques to obtain the estimations of the parameters. When either trend or spatial effects are fixed across time, MAR performs better than DYN based on model fitting criteria and predicting ability. However, DYN is better than MAR in terms of model fitting when the spatial effect is changed in time. Finally, the real life data are modeled to validate the findings.

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