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This article introduces a dynamic spatiotemporal stochastic volatility (SV)model with explicit terms for the spatial, temporal, and spatiotemporalspillover effects. Moreover, the model includes time-invariant site-specificconstant log-volatility terms. Thus, this formulation allows to distinguishbetween spatial and temporal interactions, while each location may have adifferent volatility level. We study the statistical properties of an outcomevariable under this process and show that it introduces spatial dependence inthe outcome variable. Further, we present a Bayesian estimation procedure basedon the Markov Chain Monte Carlo (MCMC) approach using a suitable datatransformation. After providing simulation evidence on the proposed Bayesianestimator's performance, we apply the model in a highly relevant field, namelyenvironmental risk modeling. Even though there are only a few empirical studieson environmental risks, previous literature undoubtedly demonstrated theimportance of climate variation studies. For example, for local air quality inNorthern Italy in 2021, we show pronounced spatial and temporal spillovers andlarger uncertainties/risks during the winter season compared to the summerseason.

A Dynamic Spatiotemporal Stochastic Volatility Model with an Application to Environmental Risks