Functional Samples and Bootstrap for Predicting Sulfur Dioxide Levels

In this article we give enhancements of several functional techniques to forecast sulfur dioxide levels near a power plant. The data are considered as a time series of curves. Assuming a lag-one dependence, the predictions are computed using the functional kernel (with local bandwith) and the linear autoregressive Hilbertian model. We carry out the estimation with a so-called “historical matrix,” which is a subsample that emphasizes uncommon shapes. We introduce a bootstrap method to evaluate the range of the forecasts, which uses Fraiman and Muniz’s order for functional data. Finally, we compare our functional techniques with neural networks and semiparametric methods, and find that the former models are often more effective.