  Air pollution is a serious issue that currently affects many industrial
cities in the world and can cause severe illness to the population. In
particular, it has been proven that extreme high levels of airborne
contaminants have dangerous short-term effects on human health, in terms of
increased hospital admissions for cardiovascular and respiratory diseases and
increased mortality risk. For these reasons, accurate estimation and prediction
of airborne pollutant concentration is crucial. In this paper, we propose a
flexible novel approach to model hourly measurements of fine particulate matter
and meteorological data collected in Beijing in 2014. We show that the standard
state space model, based on Gaussian assumptions, does not correctly capture
the time dynamics of the observations. Therefore, we propose a non-linear
non-Gaussian state space model where both the observation and the state
equations are defined by copula specifications, and we perform Bayesian
inference using the Hamiltonian Monte Carlo method. The proposed copula state
space approach is very flexible, since it allows us to separately model the
marginals and to accommodate a wide variety of dependence structures in the
data dynamics. We show that the proposed approach allows us not only to predict
particulate matter measurements, but also to investigate the effects of user
specified climate scenarios.
