Finite dimensional (FD) models \(X_d\) , i.e., deterministic functions of time and finite sets of d random variables, are developed for a class of nonstationary processes X, referred to as harmonizable. The FD models are based on Karhunen-Loève and spectral representations of X. Conditions are established under which distributions of extremes of X can be approximated by those of extremes of \(X_d\) provided that the stochastic dimension d is sufficiently large. FD models are constructed for monochromatic, Brownian motion and Ornstein-Uhlenbeck processes. Numerical results suggest that their extremes can be used as surrogates for the extremes of these processes in agreement with our theoretical findings.
