Multidimensional Stationary Time Series

This book gives a brief survey of the theory of multidimensional (multivariate), weakly stationary time series, with emphasis on dimension reduction and prediction. Understanding the covered material requires a certain mathematical maturity, a degree ofknowledge in probability theory, linear algebra, and also in real, complex and functional analysis. For this, the cited literature and the Appendix contain all necessary material. The main tools of the book include harmonic analysis, some abstract algebra, and state space methods: linear time-invariant filters, factorization of rational spectral densities, and methods that reduce the rank of the spectral density matrix--