Estimation and Simulation of Autoregressive Hilbertian Processes with Exogenous Variables

We present the autoregressive Hilbertian with exogenous variables model (ARHX) which intends to take into account the dependence structure of random curves viewed as H-valued random variables, where H is a Hilbert space of functions, under the influence of explanatory variables. Limit theorems and consistent estimators are derived from an autoregressive representation. A simulation study illustrates the accuracy of the estimation by making a comparison on forecasts with other functional models.