  For a multivariate stationary process, we develop explicit representations
for the finite predictor coefficient matrices, the finite prediction error
covariance matrices and the partial autocorrelation function (PACF) in terms of
the Fourier coefficients of its phase function in the spectral domain. The
derivation is based on a novel alternating projection technique and the use of
the forward and backward innovations corresponding to the predictions based on
the infinite past and future, respectively. We show that such representations
are ideal for studying the rates of convergence of the finite predictor
coefficients, prediction error covariances, and the PACF as well as for proving
a multivariate version of Baxter's inequality for a multivariate FARIMA process
with a common fractional differencing order for all components of the process.
