  Predicting the occurrence, level and duration of high air pollution
concentrations exceeding a given critical level enables researchers to study
the health impact of road traffic on local air quality and to inform public
policy action. Precise estimates of the probabilities of occurrence and level
of extreme concentrations are formidable due to the combination of complex
physical and chemical processes involved. This underpins the need for
developing sophisticated extreme value models, in particular allowing for
non-stationarity of environmental time series. In this paper, extremes of
nitrogen oxide (NO), nitrogen dioxide (NO$_2$) and ozone (O$_3$) concentrations
are investigated using two models. Model I is based on an extended
peaks-over-threshold (POT) approach developed by A. C. Davison and R. L. Smith,
whereby the parameters of the underlying generalized Pareto distribution (GPD)
are treated as functions of covariates (i.e., traffic and meteorological
factors). The new Model II resolves the lack of threshold stability in the
Davison--Smith model by constructing a special functional form for the GPD
parameters. For each of the models, the effects of trafic and meteorological
factors on the frequency and size of extreme values are estimated using Markov
chain Monte Carlo methods. Finally, appropriate goodness-of-fit tests and model
selection criteria confirm that Model II significantly outperforms Model I in
estimation and forecasting of extremes.
