The above GLS criterion is employed to jointly estimate all the parameters associated with the model: Kx, Kβ, b and ϕ. One possibility to alleviate the computational burden is to separate the estimation of the dependence structure (ϕ) from the parameters associated to the regression (Kx, Kβ, b) in an iterative way (called iGLS) as it is done in multivariate regression. The iGLS proven to be equivalent to classical GLS (see, for instance, ). Additionally, the method could consider more flexible dependence models (for instance, selecting the order of an AR instead of fixing it in advance) that avoid the risk of misspecification in the dependence structure. We extend this procedure to the functional regression in the following iterative procedure (called functional iGLS): Begin with a preliminary estimation of ϕ^=ϕ0 (for instance, ϕ0 = 0). Compute W^.Estimate bΣ=(Z′W^Z)-1Z′W^yBased on the residuals, e^=(y-ZbΣ), update ϕ^=ρ(e^) (and consequently, W^) where ρ is subject to the dependence structure chosen.Repeat steps 2 and 3 until convergence (small changes in bΣ and/or ϕ^)