Elements of Multivariate Time Series Analysis: (Springer Series in Statistics)

Now available in paperback. Elements of Multivariate Time Series Analysis, Second Edition introduces the basic concepts and methods that are useful in the analysis and modeling of multivariate time series data that may arise in business and economics, engineering, geophysical sciences, and other fields. The book concentrates on the time-domain analysis of multivariate time series, and assumes a background in univariate time series analysis. It covers 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, and other model specification methods useful for model building and model checking. In this revised edition, additional topics have been added and parts of the first edition have been expanded. The most notable addition is a new chapter that discusses topics that arise when exogenous variables are involved in model structures, generally through consideration of the ARMAX models. The book also includes exercise sets and multivariate time series data sets. In addition to serving as a textbook, this book will also be useful to researchers and graduate students in the areas of statistics, econometrics, business, and engineering.

Table of Contents:
1. Vector Time Series and Model Representations.- 1.1 Stationary Multivariate Time Series and Their Properties.- 1.2 Linear Model Representations for a Stationary Vector Process.- A1 Appendix: Review of Multivariate Normal Distribution and Related Topics.- A l. l Review of Some Basic Matrix Theory Results.- A l. 2 Vec Operator and Kronecker Products of Matrices.- A l. 3 Expected Values and Covariance Matrices of Random Vectors.- A1.4 The Multivariate Normal Distribution.- A1.5 Some Basic Results on Stochastic Convergence.- 2. Vector ARMA Time Series Models and Forecasting.- 2.1 Vector Moving Average Models.- 2.2 Vector Autoregressive Models.- 2.3 Vector Mixed Autoregressive Moving Average Models.- 2.4 Nonstationary Vector ARMA Models.- 2.5 Prediction for Vector ARMA Models.- 2.6 State-Space Form of the Vector ARMA Model.- A2 Appendix: Methods for Obtaining Autoregressive and Moving Average Parameters from Covariance Matrices.- A2.1 Iterative Algorithm for Factorization of Moving Average Spectral Density Matrix in Terms of Covariance Matrices.- A2.2 Autoregressive and Moving Average Parameter Matrices in Terms of Covariance Matrices for the Vector ARMA Model.- A2.3 Evaluation of Covariance Matrices in Terms of the AR and MA Parameters for the Vector ARMA Model.- 3. Canonical Structure of Vector ARMA Models.- 3.1 Consideration of Kronecker Structure for Vector ARMA Models.- 3.2 Canonical Correlation Structure for ARMA Time Series.- 3.3 Partial Autoregressive and Partial Correlation Matrices.- 4. Initial Model Building and Least Squares Estimation for Vector AR Models.- 4.1 Sample Cross-Covariance and Correlation Matrices and Their Properties.- 4.2 Sample Partial AR and Partial Correlation Matrices and Their Properties.- 4.3 Conditional Least Squares Estimation of Vector AR Models.- 4.4 Relation of LSE to Yule-Walker Estimate for Vector AR Models.- 4.5 Additional Techniques for Specification of Vector ARMA Models.- A4 Appendix: Review of the General Multivariate Linear Regression Model.- A4.1 Properties of the Maximum Likelihood Estimator of the Regression Matrix.- A4.2 Likelihood Ratio Test of Linear Hypothesis About Regression Coefficients.- A4.3 Asymptotically Equivalent Forms of the Test of Linear Hypothesis.- A4.4 Multivariate Linear Model with Reduced-Rank Structure.- A4.5 Generalization to Seemingly Unrelated Regressions Model.- 5. Maximum Likelihood Estimation and Model Checking for Vector ARMA Models.- 5.1 Conditional Maximum Likelihood Estimation for Vector ARMA Models.- 5.2 ML Estimation and LR Testing of ARMA Models Under Linear Restrictions.- 5.3 Exact Likelihood Function for Vector ARMA Models.- 5.4 Innovations Form of the Exact Likelihood Function for ARMA Models.- 5.5 Overall Checking for Model Adequacy.- 5.6 Effects of Parameter Estimation Errors on Prediction Properties.- 5.7 Motivation for AIC as Criterion for Model Selection, and Corrected Versions of AIC.- 5.8 Numerical Examples.- 6. Reduced-Rank and Nonstationary Cointegrated Models.- 6.1 Nested Reduced-Rank AR Models and Partial Canonical Correlation Analysis.- 6.2 Review of Estimation and Testing for Nonstationarity (Unit Roots) in Univariate ARIMA Models.- 6.3 Nonstationary (Unit-Root) Multivariate AR Models, Estimation, and Testing.- 6.4 A Canonical Analysis for Vector Autoregressive Time Series.- 6.5 Multiplicative Seasonal Vector ARMA Models.- 7. State-Space Models, Kaiman Filtering, and Related Topics.- 7.1 State-Variable Models and Kaiman Filtering.- 7.2 State-Variable Representations of the Vector ARMA Model.- 7.3 Exact Likelihood Estimation for Vector ARMAProcesses with Missing Values.- 7.4 Classical Approach to Smoothing and Filtering of Time Series.- 8. Linear Models with Exogenous Variables.- 8.1 Representations of Linear Models with Exogenous Variables.- 8.2 Forecasting in ARMAX Models.- 8.3 Optimal Feedback Control in ARMAX Models.- 8.4 Model Specification, ML Estimation, and Model Checking for ARMAX Models.- 8.5 Numerical Example.- Appendix: Time Series Data Sets.- Exercises and Problems.- References.- Author Index.