Operator theory proves to be a powerfull investigation tool in prediction theory helping to extend the multivariate case to the infinite-variate one. Taking the state space in the general context of an L(ε) -module H, some conditions are obtained for the action of L(ε) on H to find the best approximation of an element of H with respect to a submodule. For a harmonizable non-stationary process in a complete correlated action,using operator theory methods, a stationary investigation is given. Each harmonizable process has a spectrum obtained by its semispectral measure, and can be estimated by moving averages.
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