Abstract: Fine particulate matter (PM_2.5) has become a great concern worldwide due to its adverse health effects. PM_2.5 concentrations typically exhibit complex spatio-temporal variations. Both the mean and the spatio-temporal dependence evolve with time due to seasonality, which makes the statistical analysis of PM_2.5 challenging. In geostatistics, Gaussian process is a powerful tool for characterizing and predicting such spatio-temporal dynamics, for which the specification of a spatio-temporal covariance function is the key. While the extant literature offers a wide range of choices for flexible stationary spatio-temporal covariance models, the temporally evolving spatio-temporal dependence has received scant attention only. To this end, we propose a time-varying spatio-temporal covariance model for describing the time-evolving spatio-temporal dependence in PM_2.5 concentrations. The proposed model is shown to outperform traditionally used models through simulation studies in terms of predictions. We apply our model to analyze the PM_2.5 data in the state of Oregon, US. Therein, we show that the spatial scale and smoothness exhibit noticeable temporal variation. The proposed model is also shown to be beneficial over traditionally used models on this dataset for predictions.

Key words and phrases: Bernstein functions, Matérn covariance function, nonstationarity, spatio-temporal covariance.