In this revised edition, some additional topics have been added to the original version, and certain existing materials have been expanded, in an attempt to pro vide a more complete coverage of the topics of time-domain multivariate time series modeling and analysis. The most notable new addition is an entirely new chapter that gives accounts on various topics that arise when exogenous vari ables are involved in the model structures, generally through consideration of the so-called ARMAX models; this includes some consideration of multivariate linear regression models with ARMA noise structure for the errors. Some other new material consists of the inclusion of a new Section 2. 6, which introduces state-space forms of the vector ARMA model at an earlier stage so that readers have some exposure to this important concept much sooner than in the first edi tion; a new Appendix A2, which provides explicit details concerning the rela tionships between the autoregressive (AR) and moving average (MA) parameter coefficient matrices and the corresponding covariance matrices of a vector ARMA process, with descriptions of methods to compute the covariance matrices in terms of the AR and MA parameter matrices; a new Section 5.