Elements of Multivariate Time Series Analysis - Paperback

EAN (ISBN-13): 9780387406190
ISBN (ISBN-10): 0387406190
Hardcover
Paperback
Publishing year: 2003
Publisher: Springer New York
357 Pages
Weight: 0,526 kg
Language: eng/Englisch

Book in our database since 2007-07-10T20:06:02+01:00 (London)
Detail page last modified on 2023-04-21T10:54:49+01:00 (London)
ISBN/EAN: 9780387406190

ISBN - alternate spelling:
0-387-40619-0, 978-0-387-40619-0
Alternate spelling and related search-keywords:
Book author: gregory, springer
Book title: time series analysis, springer series, multivariate statistic, analysis element, time goes, how tell time, elements

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Information from Publisher

Author: Gregory C. Reinsel
Title: Springer Series in Statistics; Elements of Multivariate Time Series Analysis
Publisher: Springer; Springer US
358 Pages
Publishing year: 2003-10-31
New York; NY; US
Language: English
53,49 € (DE)
54,99 € (AT)
59,00 CHF (CH)
Available
XVII, 358 p.

BC; Hardcover, Softcover / Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik; Wahrscheinlichkeitsrechnung und Statistik; Verstehen; Statistical Theory and Methods; BB

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.