Maximum ozone concentration forecasting by functional non-parametric approaches
Résumé
Prediction of maximum ozone concentration is of great importance, especially to alert the population and to allow the authorities to take preventive measures soon enough. Ozone concentration and meteoro-logical variables are now observed each hour or every 10 min so that we nearly get continuous observations along time, i.e. functions, as covariates. Much work has been done in the statistical community to propose effective models for predicting ozone concentration one day ahead, but there has been much less effort to study methods that take the functional nature of these data into account. We propose here two non-linear models based on kernel estimators that handle the functional characteristics of the data by means of a measure of proximity between observed functions. In addition, we use additive ideas to take exogeneous variables into account without being too sensitive to dimensionality effects. Such procedures are called multivariate functional non-parametric approaches, since our models/estimates are non-parametric (because of the non-linear structure linking the explanatory and the response variables), functional (because the variables are curves) and multi-dimensional (because we can have many functional explanatory variables). These models are used to forecast maximum ozone concentration in Toulouse (France). We compare them to more classical techniques and the results are promising.