Spatiotemporal dynamic quantile regression models with applications to particulate matter concentration data

Abstract

The spatiotemporal evolution of high-concentration PM₂.₅ is a significant concern, especially when working with datasets that display complex spatiotemporal dependencies. Identifying the spatiotemporal covariance function in such cases is often challenging. The paper proposes a novel spatiotemporal dynamic quantile regression model (STDQM) that captures the temporal evolution of spatial processes by integrating a latent Gaussian process. To accommodate more complex data structures and expand the inferential capabilities of the asymmetric Laplace distribution within the standard quantile regression framework, the paper also proposes a more flexible STDQM based on the generalized asymmetric Laplace distribution. A substantial number of simulation studies demonstrate that the proposed methods significantly enhance inference quality and prediction accuracy compared to existing alternative methods. The new method is employed to analyse the influencing factors and spatiotemporal evolution of PM₂.₅ concentrations at various quantile levels in Lombardy, Italy, from 2016 to 2021.