On the construction of Wold decomposition for multivariate stationary processes

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 membership, variant] Z, onto its component processes , k [set membership, variant] Z, j = 1, ..., q. The method does not give a complete solution to the Wold decomposition problem.