The functional generalized least squares regression (FGLS) model between two centered variables (E(y)=0, E(X)=0) states that y=⟨X,β⟩+ϵ=∫TX(t)β(t)dt+ϵ(2) where βϵL2(T) and ϵ is now a random vector with mean 0 and covariance matrix Ω=E(ϵϵ′). This model includes, as its special cases, many others models, all of them based on Ω = Ω(ϕ) = σ2 Σ(ϕ), where ϕ is the parameter associated with the dependence structure of Ω. Some classical examples are presented in the following models: Equi-correlated model: Var(ϵi)=σ2 and Cov(ϵi, ϵj) = σ2 ϕ, i ≠ j, ϕ ∈ (−1, 1)Heteroskedastic block model: Ω=diag(σ12In1|σ22In2|⋯|σp2Inp) with n1 + n2 + ⋯ + np = nAR(1) model: ϵi = ϕϵi−1 + εi with |ϕ| < 1, E(εi)=0, Var(εi)=τ2 and Cov(εi, εj) = 0, i ≠ j Ω=τ21−ϕ2(ϕ|i−j|)i,j=1nThe variance structure is also known for every ARMA(p,q) model.Spatial correlation model: Ω=σ2(ρ(d(si,sj))) where si,sj are, respectively, the locations for i, j; and ρ is the spatial correlation function.