On relations between prediction error covariance of univariate and multivariate processes

By using results pertaining to prediction of univariate stationary processes we express [Sigma], the one-step ahead prediction error covariance matrix of a multivariate procces in terms of its spectral density matrix [latin small letter f with hook]x. This sheds some light on a problem of Wiener and Masani (1957). Alternatively, by relying on results from interpolation of multivariate processes, we obtain closed-form and applicable formulae for the interpolators and their errors for a stretch of missing values of univariate processes.