Springer Statistics

By: Gregory C. Reinsel

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Paperback | 2 December 2003 | Edition Number 2

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380 Pages

Edition Type
Revised

Dimensions(cm)
22.86 x 15.24 x 1.91

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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.

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Preface
Vector Time Series and Model Representations	p. 1
Stationary Multivariate Time Series and Their Properties	p. 2
Linear Model Representations for a Stationary Vector Process	p. 7
A1 Appendix: Review of Multivariate Normal Distribution and Related Topics	p. 12
Vector ARMA Time Series Models and Forecasting	p. 21
Vector Moving Average Models	p. 21
Vector Autoregressive Models	p. 26
Vector Mixed Autoregressive Moving Average Models	p. 33
Nonstationary Vector ARMA Models	p. 40
Prediction for Vector ARMA Models	p. 45
Canonical Structure of Vector ARMA Models	p. 52
Consideration of Kronecker Structure for Vector ARMA Models	p. 52
Canonical Correlation Structure for ARMA Time Series	p. 58
Partial Autoregressive and Partial Correlation Matrices	p. 64
Initial Model Building and Least Squares Estimation for Vector AR Models	p. 74
Sample Cross-Covariance and Correlation Matrices and Their Properties	p. 74
Sample Partial AR and Partial Correlation Matrices and Their Properties	p. 78
Conditional Least Squares Estimation of Vector AR Models	p. 80
Relation of LSE to Yule-Walker Estimate for Vector AR Models	p. 89
Additional Techniques for Specification of Vector ARMA Models	p. 91
A4 Appendix: Review of the General Multivariate Linear Regression Model	p. 105
Maximum Likelihood Estimation and Model Checking for Vector ARMA Models	p. 111
Conditional Maximum Likelihood Estimation for Vector ARMA Models	p. 111
ML Estimation and LR Testing of ARMA Models Under Linear Restrictions	p. 118
Exact Likelihood Function for Vector ARMA Models	p. 122
Innovations Form of the Exact Likelihood Function for ARMA Models	p. 129
Overall Checking for Model Adequacy	p. 132
Effects of Parameter Estimation Errors on Prediction Properties	p. 138
Numerical Examples	p. 142
Reduced-Rank and Nonstationary Co-integrated Models	p. 154
Nested Reduced-Rank AR Models and Partial Canonical Correlation Analysis	p. 154
Review of Estimation and Testing for Nonstationarity (Unit Roots) in Univariate ARIMA Models	p. 162
Nonstationary (Unit-Root) Multivariate AR Models, Estimation, and Testing	p. 165
Multiplicative Seasonal Vector ARMA Models	p. 186
State-Space Models, Kalman Filtering, and Related Topics	p. 192
State-Variable Models and Kalman Filtering	p. 192
State-Variable Representations of the Vector ARMA Model	p. 198
Exact Likelihood Estimation for Vector ARMA Processes with Missing Values	p. 215
Classical Approach to Smoothing and Filtering of Time Series	p. 218
Appendix: Time Series Data Sets	p. 226
Exercises and Problems	p. 238
References	p. 248
Index	p. 257
Table of Contents provided by Blackwell. All Rights Reserved.

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