ON HANKEL-NORM APPROXIMATION OF STATIONARY INCREMENT PROCESSES.

We consider the problem of approximating stationary increment processes minimizing the prediction error when the prediction of functionals of the whole future is considered. It is shown that this approach leads very naturally to the Hankel norm approximation of a spectral factor of left brace y(t) right brace . Some ordering and interlocking properties for the singular values of the Hankel operators corresponding to approximations of different spectral factors are derived. It is in particular shown that the minimum phase model leads to a better accuracy in the approximation than any other model. We eventually show that the Hankel norm error provides a bound on the mean square error when the increments of the process are considered.