Minimax statistical models for air pollution time series. Application to ozone time series data measured in Bordeaux

This paper deals with the application of l(infinity) (or minimax) optimization techniques to statistical modelling of high frequency air pollution data. The method was applied to ground-level ozone time-series data measured in Bordeaux over 4 years from 1998 to 2001. The aim of model building was to develop predictive models in order to provide forecasts of the maximal daily ground-level ozone concentration. Experimental results from this case study indicate that such techniques could be more appropriate than the commonly used l2 setting if only good estimation of high levels is of interest. When the free parameters are fitted by means of l(infinity) optimization techniques, the forecasting errors are more evenly distributed amongst the data points, resulting in a better estimation of high values. The paper compares the quality of forecasts produced by both a linear and a nonlinear model, using l2 and l(infinity) parameter optimization.