Factorization of a Spectral Density with Smooth Eigenvalues of a Multidimensional Stationary Time Series

The aim of this paper to give a multidimensional version the classical one-dimensional case smooth spectral density. A density with eigenvalues and H∞ eigenvectors gives an explicit method factorize compute Wold representation weakly stationary time series. formula, similar Kolmogorov–Szego” is given for covariance matrix innovations. These results are important best linear predictions applicable when rank process smaller than dimension process, which occurs frequently in many current applications, including econometrics.