Modelling multivariate pollutant time series with wavelet functions

This paper deals with a new approach based on wavelet functions to model multivariate time series. Time series are formalised in terms of NARX (Non Linear Auto Regressive with eXogenous inputs) models and the vector of unknown parameters is determined by using a genetic algorithms (GAs) optimisation approach, since GAs allow finding the global minimum of a function with many variables, overcoming the limitation of typical gradient based techniques. A case study, referring to the modelling of daily averages of SO2 time series recorded in the industrial area of Syracuse (Italy) is reported. The performance of the proposed approach is compared with other traditional approaches such as ARX and Multi-layer neural networks. The results obtained show that while there are no significant differences between the neural and the wavelet approach in terms of model performance and computational effort, there is an appreciable advantage in using the proposed technique in terms of internal model complexity.