Elements of Multivariate Time Series Analysis [Paperback]

Now available in paperback, this book introduces basic concepts and methods useful in the analysis and modeling of multivariate time series data. It concentrates on the time-domain analysis of multivariate time series, and assumes univariate time series analysis, while covering basic topics such as stationary processes and their covariance matrix structure, vector AR, MA, and ARMA models, forecasting, least squares and maximum likelihood estimation for ARMA models, associated likelihood ratio testing procedures.

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 5.1. Vector Time Series and Model Representations.- 1.1 Stationary Multivariate Time Series and Their Properties.- 1.1.1 Covariance and Correlation Matrices for a Stationary Vector Process.- 1.1.2 Some Spectral Characteristics fls$