A Bayesian Non-linear State Space Copula Model to Predict Air Pollution in Beijing
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Air pollution is a serious issue that currently affects many industrial cities in the world and can cause severe illness to the population. For this reason, a correct estimation and prediction of airborn pollutant concentrations is crucial. In this paper, we analyze hourly measurements of fine particulate matter and metereological data collected in Beijing in 2014. We show that the standard state space model, based on Gaussian assumptions, does not allow to correctly capture the time dynamics of the observations. Therefore, we propose a novel 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 accomodate a wide variety of dependence structures in the data dynamics. We show that the proposed approach allows us not only to accurately predict particulate matter measurements, but also to capture unusual high levels of air pollution, which were not detected by measured effects.
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