Gregory C. Reinsel

This book provides an account of multivariate reduced-rank regression, a tool of multivariate analysis that enjoys a broad array of applications. In addition to a historical review of the topic, its connection to other widely used statistical methods, such as multivariate analysis of variance (MANOVA), discriminant analysis, principal components, canonical correlation analysis, and errors-in-variables models, is also discussed. This new edition incorporates Big Data methodology and its applications, as well as high-dimensional reduced-rank regression, generalized reduced-rank regression with complex data, and sparse and low-rank regression methods. Each chapter contains developments of basic theoretical results, as well as details on computational procedures, illustrated with numerical examples drawn from disciplines such as biochemistry, genetics, marketing, and finance. This book is designed for advanced students, practitioners, and researchers, who may deal withmoderate and high-dimensional multivariate data. Because regression is one of the most popular statistical methods, the multivariate regression analysis tools described should provide a natural way of looking at large (both cross-sectional and chronological) data sets. This book can be assigned in seminar-type courses taken by advanced graduate students in statistics, machine learning, econometrics, business, and engineering.

Praise for the Fourth Edition "The book follows faithfully the style of the original edition. The approach is heavily motivated by real-world time series, and by developing a complete approach to model building, estimation, forecasting and control."—Mathematical Reviews Bridging classical models and modern topics, the Fifth Edition of Time Series Analysis: Forecasting and Control maintains a balanced presentation of the tools for modeling and analyzing time series. Also describing the latest developments that have occurred in the field over the past decade through applications from areas such as business, finance, and engineering, the Fifth Edition continues to serve as one of the most influential and prominent works on the subject. Time Series Analysis: Forecasting and Control, Fifth Edition provides a clearly written exploration of the key methods for building, classifying, testing, and analyzing stochastic models for time series and describes their use in five important areas of application: forecasting; determining the transfer function of a system; modeling the effects of intervention events; developing multivariate dynamic models; and designing simple control schemes. Along with these classical uses, the new edition covers modern topics with new features that include: A redesigned chapter on multivariate time series analysis with an expanded treatment of Vector Autoregressive, or VAR models, along with a discussion of the analytical tools needed for modeling vector time seriesAn expanded chapter on special topics covering unit root testing, time-varying volatility models such as ARCH and GARCH, nonlinear time series models, and long memory modelsNumerous examples drawn from finance, economics, engineering, and other related fieldsThe use of the publicly available R software for graphical illustrations and numerical calculations along with scripts that demonstrate the use of R for model building and forecastingUpdates to literature references throughout and new end-of-chapter exercisesStreamlined chapter introductions and revisions that update and enhance the exposition Time Series Analysis: Forecasting and Control, Fifth Edition is a valuable real-world reference for researchers and practitioners in time series analysis, econometrics, finance, and related fields. The book is also an excellent textbook for beginning graduate-level courses in advanced statistics, mathematics, economics, finance, engineering, and physics.

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.