Predicting seasonal influenza transmission using Regression Models with Temporal Dependence

In this manuscript, we use meteorological information in Galicia (Spain) to propose a novel approach to predict the incidence of influenza. Our approach extends the GLS methods in the multivariate framework to functional regression models with dependent errors. A simulation study shows that the GLS estimators render better estimations of the parameters associated with the regression model and obtain extremely good results from the predictive point of view. Thus they improve the classical linear approach. It proposes an iterative version of the GLS estimator (called iGLS) that can help to model complicated dependence structures, uses the distance correlation measure $\mathcal{R}$ to select relevant information to predict influenza rate and applies the GLS procedure to the prediction of the influenza rate using readily available functional variables. These kinds of models are extremely useful to health managers in allocating resources in advance for an epidemic outbreak.