分位數預測方法因能有效描述條件分布中不同位置的特性，因此已被廣泛應用於 非高斯資料的建模與預測。然而，在許多實務應用中，資料通常同時具有偏態、厚 尾、極端值以及空間相關性等特徵。在此情況下，若傳統分位數預測方法未能納入空 間交互作用，則容易導致估計不穩定與預測準確度下降，尤其當資料存在明顯空間異 質性時，此問題會更加顯著。為克服上述挑戰，本文提出一套結合空間資訊與機率狀 態轉移加權機制的空間分位數預測架構。所提出的方法包含三個核心組成：首先，利 用核函數型空間分位數估計量，以整合鄰近位置的資訊並提升估計穩定性；其次，透 過分位數型態的狀態表示方式來描述不同的分布區間；最後，建立機率狀態轉移權重 矩陣，以動態整合不同分位數下的預測結果。藉由上述機制，所提出的方法能更具彈 性且穩健地處理空間異質性與非高斯分布特徵。本文進一步在多種非高斯情境下進行 模擬研究，包括厚尾分布與偏態分布等設定。模擬結果顯示，相較於既有方法，所提 出的方法能有效提升預測穩定性並降低預測誤差，尤其在極端分位數預測上具有更佳 表現。最後，本文將所提出的預測架構應用於台灣 2019 至 2024 年每日 PM2.5 濃度資 料。實證結果顯示，此方法能有效捕捉空氣污染的時空變動特性，並提升極端污染事 件預測的可靠性，進一步驗證其於環境風險評估上的實務應用價值;Quantile-based forecasting methods have been widely used for modeling non-Gaussian data due to their ability to characterize different parts of conditional distributions. However， in many real-world applications， datasets often simultaneously exhibit skewness， heavy-tailed behavior， extreme observations， and spatial dependence. Under such settings， conventional quantile forecasting approaches that ignore spatial interactions may suffer from unstable estimation and reduced predictive accuracy， particularly in the presence of substantial spatial heterogeneity. To address these challenges， this study develops a spatial quantile forecasting framework that integrates spatial information with probabilistic state-transition weighting mechanisms. The proposed approach extends existing quantile forecasting methods by incorporating three key components: a kernel-based spatial quantile estimator to borrow information from neighboring locations， a quantile-based state representation to characterize distributional regimes， and a probabilistic state-transition weight matrix to dynamically combine quantile-specific forecasts across different distributional states. Through these components， the proposed framework is able to adapt to spatial heterogeneity and non-Gaussian distributional features in a flexible and robust manner. Extensive simulation studies are conducted under various non-Gaussian settings， including heavy-tailed and skewed distributions. The results demonstrate that the proposed method substantially improves forecasting stability and reduces prediction errors compared with existing approaches， particularly for extreme quantile forecasting. Finally， the proposed framework is applied to Taiwan’s daily PM$_{2.5}$ concentration data from 2019 to 2024. The empirical analysis shows that the proposed method effectively captures the spatiotemporal variability of air pollution and improves the reliability of extreme pollution forecasts， confirming its practical value for environmental risk assessment.
