Necessary and sufficient conditions for an arbitrary q-variate stationary sequence xt, t [set membership, variant] , to be deterministic are presented. A characterization of the rank r(x) of xt, t [set membership, variant] , and a method to construct the Wold-Cramér decomposition for xt, t [set...

A method to construct the Wold decomposition for multivariate stationary stochastic processes xk, k [set membership, variant] Z, is presented. The method is based on orthogonal decompositions for xk, k [set membership, variant] Z, obtained by forming orthogonal projections of xk, k [set...