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AuthorReinsel, Gregory C. author
TitleElements of Multivariate Time Series Analysis [electronic resource] / by Gregory C. Reinsel
ImprintNew York, NY : Springer US, 1993
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Descript XIV, 263 p. online resource


The use of methods of time series analysis in the study of multivariate time series has become of increased interest in recent years. Although the methods are rather well developed and understood for univarjate time series analysis, the situation is not so complete for the multivariate case. This book is designed to introduce the basic concepts and methods that are useful in the analysis and modeling of multivariate time series, with illustrations of these basic ideas. The development includes both traditional topics such as autocovariance and autoยญ correlation matrices of stationary processes, properties of vector ARMA models, forecasting ARMA processes, least squares and maximum likelihood estimation techniques for vector AR and ARMA models, and model checking diagnostics for residuals, as well as topics of more recent interest for vector ARMA models such as reduced rank structure, structural indices, scalar component models, canonical correlation analyses for vector time series, multivariate unit-root models and cointegration structure, and state-space models and Kalman filtering techniques and applications. This book concentrates on the time-domain analysis of multivariate time series, and the important subject of spectral analysis is not considered here. For that topic, the reader is referred to the excellent books by Jenkins and Watts (1968), Hannan (1970), Priestley (1981), and others


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

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