Sequential approximation of stochastic processes with guaranteed propeties

Given the Covariance function R(i, j), 1≤i, j≤N, of a discrete time vector valued random process y(i), we consider the problem of approximating the process realization with a fixed (lower) order model. The approximate model is chosen so that statistical bounds are guaranteed in the estimation of the process. A sequential design procedure as N grows, based on the minimization of an approximation measure, is proposed in the paper and conditions for convergence of the algorithm when N→∞ are indicated.