Any weakly stationary time series X(t) can be looked upon as a superposition of an infinite number of harmonic oscillations. Let (t) be a finite linear combinations of oscillations with frequencies λ_j = jδ by trigonometric interpolation of the values of X (k·δt), (t) becomes a discrete approximation of X(t). Various representation for (t) allows an analysis of the mean square error   at any time t. By interpolating the“weighted” values z_kX (k·δt) instead of X (k·δt), the error may be influenced by an appropriate choice of the weights: specific weights are attached to any nonempty set P that minimize the error function f_p if a prediction of X(t) on P is required. The cases   are discussed (μ denotes a finite measure on P).