Maximum ozone concentration forecasting by functional non‐parametric approaches

Abstract

SUMMARYPrediction 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.

Smoothing splines estimators for functional linear regression

“…The concentration of specific pollutants as well as meteorological variables are measured each hour. Some previous studies using the same data are described in Cardot, Crambes and Sarda [6] and Aneiros-Perez et al [1].…”

Modelling functional additive quantile regression using support vector machines approach

“…However, it is difficult to compare the prediction results obtained by our approach with other predictions methods by Aneiros-Perez et al (2004) and Ferraty and Vieu (2009) because of the random effect of the generation of the test and the learning samples.…”

“…Data are missing for 22 days for technical reasons. These data are more deeply presented and treated with other methods in Aneiros-Perez, Cardot, Perez, and Vieu (2004), Cardot, Crambes, and Sarda (2007) and Ferraty and Vieu (2009). There are five functional covariates which are daily curves measured each hour.…”

Forecasting Distributions of Inflation Rates: the Functional Auto-Regressive Approach

“…Cardot et al (1999Cardot et al ( , 2007 and Mas (2007) refined the asymptotic theory. Early applications were in forecasting climate patterns such as temperatures (Besse et al, 2000) and ozone levels (Damon and Guillas, 2002;Aneiros-Perez et al, 2004). Recently, the application has been adopted in finance.…”