The scenario (a) corresponds to a β parameter which has an exact representation respect to the first three theoretical principal components of the Wiener process. On the contrary, the β parameter for scenario (b) cannot be well represented using a small number of theoretical principal components. In both scenarios, we have used two types of basis for representing X and β: the empirical principal components basis derived from the sample (FPC) and the cubic B–splines (BSP) at equispaced knots in [0, 1]. The same basis was employed for both representations i.e. in this case Ψ = φ and Kx = Kβ. The optimal number of components (Kβ) was selected using the GCCV criterion in the range 1–8 for FPC and 5–11 for BSP.