Using stochastic volatility models to analyse weekly ozone averages in Mexico City

In this paper we make use of some stochastic volatility models to analyse the behaviour of a weekly ozone average measurements series. The models considered here have been used previously in problems related to financial time series. Two models are considered and their parameters are estimated using a Bayesian approach based on Markov chain Monte Carlo (MCMC) methods. Both models are applied to the data provided by the monitoring network of the Metropolitan Area of Mexico City. The selection of the best model for that specific data set is performed using the Deviance Information Criterion and the Conditional Predictive Ordinate method.     

Using a non-homogeneous Poisson model with spatial anisotropy and change-points to study air pollution data

Environmental and Ecological Statistics - A non-homogeneous Poisson process is used to study the rate at which a pollutant’s concentration exceeds a given threshold of interest. An...     

Comparing the Number of Ozone Exceedances in Different Seasons of the Year in Mexico City

Ozone air pollution is a serious problem in several cities of the world. Hence, to analyse the behaviour of this pollutant is a very important issue. One problem of interest is to study the behaviour of the inter-occurrences times between two ozone exceedances, i.e. between two days in which the pollutant’s measurement surpasses a given threshold. Another interest resides in comparing the behaviour of ozone measurements in different seasons of the year. In this paper we use some Poisson models to analyse this problem. The time interval at which the ozone measurements were taken is split into subintervals corresponding roughly to the seasons of the year. We consider three parametric forms for the mean of the Poisson model, and consequently for the mean of the inter-occurrences times. In each model, the parameters describing its mean are estimated using Bayesian inference via Markov chain Monte Carlo methods. The models are applied to the ozone measurements provided by the Mexico City monitoring network. Theoretical results suggest that an increase has occurred in the mean inter-exceedances times and this is corroborated by the observed data. Differences between the behaviour of the pollutant during different seasons of the year are also detected as well as similarities in the same season in different years. Besides estimating the mean of the Poisson models, inference for the possible presence and location of change-points indicating change of parameters of the model is also performed.