The GLS criterion can be employed to jointly estimate all the parameters associated to the model and can be expressed as: minKx,Kβ,b,ϕGLS=minKx,Kβ,b,ϕ(y-Zb)′Σ(ϕ)-1(y-Zb), where the parameters Kx and Kβ related to the basis for X and β are typically chosen a priori taking into account, for instance, the quality of the data and its representation on the discretization grid or other considerations related to the data-generating process (smoothness, physical restrictions, interpretability,…). The direct minimization of GLS usually cannot be affordable even though we only consider the parameters b and ϕ. The generalized cross-validation (GCV) criterion has been widely used to this end despite not being the right criterion for dependent errors. We use the generalized correlated cross-validation (GCCV) as a better alternative. This suggested criterion is an extension to GCV within the context of correlated errors proposed by Carmack et al. . It is defined as follows: GCCV(Kx,Kβ,b,ϕ)=∑i=1n(yi-y^i,b)2(1-tr(G)n)2 where G = 2H Σ(ϕ) − H Σ(ϕ)H′ takes into account the effect of the dependence, the trace of G is an estimation of the degrees of freedom consumed by the model and H is the hat matrix. The important advantage of this criterion is that it is rather easy to compute because it avoids the need to compute the inverse of the matrix Σ. Even so, the complexity of the GLS criterion depends on the structure of Σ and it could sometimes be hard either to minimize or computationally expensive.