Author | Reinsel, Gregory C. author |
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Title | Elements of Multivariate Time Series Analysis [electronic resource] / by Gregory C. Reinsel |
Imprint | New York, NY : Springer US, 1993 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-0198-1 |
Descript | XIV, 263 p. online resource |
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 -- 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 Numerical Examples -- 6. Reduced-Rank and Nonstationary Co-Integrated 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 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 -- Appendix: Time Series Data Sets -- Exercises and Problems -- References