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The inclusion of exogenous variables in functional autoregressive ozone forecasting

In this article, we propose a new technique for ozone forecasting. The approach is functional, that is we consider stochastic processes with values in function spaces. We make use of the essential characteristic of this type of phenomenon by taking into account theoretically and practically the continuous time evolution of pollution. One main methodological enhancement of this article is the incorporation of exogenous variables (wind speed and temperature) in those models. The application is carried out on a six‐year data set of hourly ozone concentrations and meteorological measurements from Béthune (France). The study examines the summer periods because of the higher values observed. We explain the non‐parametric estimation procedure for autoregressive Hilbertian models with or without exogenous variables (considering two alternative versions in this case) as well as for the functional kernel model. The comparison of all the latter models is based on up‐to‐24 hour‐ahead predictions of hourly ozone concentrations. We analyzed daily forecast curves upon several criteria of two kinds: functional ones, and aggregated ones where attention is put on the daily maximum. It appears that autoregressive Hilbertian models with exogenous variables show the best predictive power. Copyright © 2002 John Wiley & Sons, Ltd.