*Article* **Functional Location-Scale Model to Forecast Bivariate Pollution Episodes**

### **Manuel Oviedo-de La Fuente 1, Celestino Ordóñez 2,***∗* **and Javier Roca-Pardiñas 3**


Received: 7 May 2020; Accepted: 29 May 2020; Published: 8 June 2020

**Abstract:** Predicting anomalous emission of pollutants into the atmosphere well in advance is crucial for industries emitting such elements, since it allows them to take corrective measures aimed to avoid such emissions and their consequences. In this work, we propose a functional location-scale model to predict in advance pollution episodes where two pollutants are involved. Functional generalized additive models (FGAMs) are used to estimate the means and variances of the model, as well as the correlation between both pollutants. The method not only forecasts the concentrations of both pollutants, it also estimates an uncertainty region where the concentrations of both pollutants should be located, given a specific level of uncertainty. The performance of the model was evaluated using real data of SO2 and NO*x* emissions from a coal-fired power station, obtaining good results.

**Keywords:** pollution episodes; functional data; bivariate analysis; uncertainty region; generalized additive models
