Contents of Elements of Multivariate Time Series Analysis

• 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
  
  
• 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
  
  
• 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
  
  
• 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, Kalman Filtering, and Related Topics
  
  7.1 State-Variable Models and Kalman Filtering
  7.2 State-Variable Representations of the Vector ARMA Model
  7.3 Exact Likelihood Estimation for Vector ARMA Processes 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
  
• Subject Index
  
• Author Index