LAUSR

We present a method to forecast pollution episodes with a bivariate response. The method simultaneously estimates the concentrations of two pollutants, using historical data. It is based on a location–scale model where the means and the standard deviations are approximated by kernel smoothers in additive models, while the variance–covariance matrix is obtained from the residuals of the previous models. The method provides not only an estimation of the concentration of both pollutants over time but also uncertainty regions covering a specific percentage of the data. The suitability of the model was tested with both simulated and real data (specifically $$\hbox {SO}_2$$ and $$\hbox {NO}_x$$ concentrations from a coal-fired power station). The results have proved highly satisfactory in both cases. The percentage of data covered by the uncertainty region, its area and a new loss function, a variant of the pinball loss function, were used as metrics to evaluate the performance of the model.