Maximum likelihood estimation of the multivariate hidden dynamic geostatistical model with application to air quality in Apulia, Italy

Multivariate spatio-temporal statistical models are deserving for increasing attention for environmental data in general and for air quality data in particular because they can reveal dependencies and spatio-temporal dynamics across multiple variables and can be used to obtain dynamic concentration maps over specified areas. In this frame, we introduce a multivariate generalization of a known spatio-temporal model referred to as the hidden dynamic geostatistical model. Maximum likelihood parameter estimates are obtained implementing the expectation maximization algorithm and suitably extending the D-STEM software, recently introduced for alternative model specifications, allowing to handle multiple variables with heterogeneous spatial support, covariates, and missing data. A case study illustrates some of the statistical issues typical of a medium complexity problem related to air quality data modeling. Considering air quality and meteorological data over the Apulia region, Italy, the usual approach using meteorological variables as regressors is not possible because these data are observed on different monitoring networks, and preliminary spatial interpolation to co-locate the data is to be avoided. Hence, an eight-variate model is considered for understanding the relations between daily concentrations of particulate matters (PM10) and nitrogen dioxides (NO2) and six non co-located meteorological variables. Model interpretation is given, and its use for dynamic map construction, uncertainty included, is illustrated. Moreover, some preliminary evidence of the model capability to detect a Saharan dust event is presented.