Spatio‐Temporal Analysis of Extreme PM2.5 Levels in Taiwan

We investigate extremes of PM2.5$$ {}_{2.5} $$ in Taiwan using data from Environmental Protection Administration monitoring stations. The objective is to examine long‐term trends in PM2.5$$ {}_{2.5} $$ extremes and short‐term spikes, measured by daily 1‐hour maximums, as they relate to human exposure and acute health risks in daily life. To model daily 1‐hour maximum PM2.5$$ {}_{2.5} $$ concentrations across space and time, we adopt the generalized extreme value (GEV) distribution. Extending beyond location‐specific temporal extreme‐value models, we develop a spatio‐temporal varying‐coefficient GEV framework in which the distributional parameters evolve smoothly over space and time through spatio‐temporal basis functions. This formulation leverages information from neighboring sites and adjacent times, enabling the model to capture both broad‐scale structures and localized variability in extremes. The framework yields marginal distributions of extreme PM2.5$$ {}_{2.5} $$ at any location and time, accounting for spatial heterogeneity, seasonal dynamics, and irregular data availability. The method is computationally efficient and can be implemented with existing R packages. Application to Taiwanese air‐quality data reveals a general decline in extreme PM2.5$$ {}_{2.5} $$ events over the past decade, though substantial regional variability persists across Taiwan.