| Description |
1 online resource (xxi, 764 pages) : illustrations |
| Contents |
1. Objectives of Analyzing Multiple Time Series -- Some Basics -- Vector Autoregressive Processes -- Outline of the Following Chapters -- Part I. Finite Order Vector Autoregressive Processes -- 2. Stable Vector Autoregressive Processes -- Basic Assumptions and Properties of VAR Processes -- Stable VAR(p) Processes -- The Moving Average Representation of a VAR Process -- Stationary Processes -- Computation of Autocovariances and Autocorrelations of Stable VAR Processes -- Forecasting -- The Loss Function -- Point Forecasts -- Interval Forecasts and Forecast Regions -- Structural Analysis with VAR Models -- Granger-Causality, Instantaneous Causality, and Multi-Step Causality -- Impulse Response Analysis -- Forecast Error Variance Decomposition -- Remarks on the Interpretation of VAR Models -- 3. Estimation of Vector Autoregressive Processes -- Multivariate Least Squares Estimation -- The Estimator -- Asymptotic Properties of the Least Squares Estimator |
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Small Sample Properties of the LS Estimator -- Least Squares Estimation with Mean-Adjusted Data and Yule-Walker Estimation -- Estimation when the Process Mean Is Known -- Estimation of the Process Mean -- Estimation with Unknown Process Mean -- The Yule-Walker Estimator -- Maximum Likelihood Estimation -- The Likelihood Function -- The ML Estimators -- Properties of the ML Estimators -- Forecasting with Estimated Processes -- General Assumptions and Results -- The Approximate MSE Matrix -- A Small Sample Investigation -- Testing for Causality -- A Wald Test for Granger-Causality -- Testing for Instantaneous Causality -- Testing for Multi-Step Causality -- The Asymptotic Distributions of Impulse Responses and Forecast Error Variance Decompositions -- The Main Results -- Proof of Proposition 3.6 -- Investigating the Distributions of the Impulse Responses by Simulation Techniques -- Algebraic Problems -- Numerical Problems -- 4 . VAR Order Selection and Checking the Model Adequacy |
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A Sequence of Tests for Determining the VAR Order -- The Impact of the Fitted VAR Order on the Forecast MSE -- The Likelihood Ratio Test Statistic -- A Testing Scheme for VAR Order Determination -- Criteria for VAR Order Selection -- Minimizing the Forecast MSE -- Consistent Order Selection -- Comparison of Order Selection Criteria -- Some Small Sample Simulation Results -- Checking the Whiteness of the Residuals -- The Asymptotic Distributions of the Autocovariances and Autocorrelations of a White Noise Process -- The Asymptotic Distributions of the Residual Autocovariances and Autocorrelations of an Estimated VAR Process -- Portmanteau Tests -- Lagrange Multiplier Tests -- Testing for Nonnormality -- Tests for Nonnormality of a Vector White Noise Process -- Tests for Nonnormality of a VAR Process -- Tests for Structural Change -- Chow Tests -- Forecast Tests for Structural Change -- Algebraic Problems -- Numerical Problems -- 5. VAR Processes with Parameter Constraints |
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Linear Constraints -- The Model and the Constraints -- LS, GLS, and EGLS Estimation -- Maximum Likelihood Estimation -- Constraints for Individual Equations -- Restrictions for the White Noise Covariance Matrix -- Forecasting -- Impulse Response Analysis and Forecast Error Variance Decomposition -- Specification of Subset VAR Models -- Model Checking -- VAR Processes with Nonlinear Parameter Restrictions -- Bayesian Estimation -- Basic Terms and Notation -- Normal Priors for the Parameters of a Gaussian VAR Process -- The Minnesota or Litterman Prior -- Practical Considerations -- Classical versus Bayesian Interpretation of {macr}[alpha] in Forecasting and Structural Analysis -- Algebraic Exercises -- Numerical Problems -- Part II. Cointegrated Processes -- 6. Vector Error Correction Models -- Integrated Processes -- VAR Processes with Integrated Variables -- Cointegrated Processes, Common Stochastic Trends, and Vector Error Correction Models -- Deterministic Terms in Cointegrated Processes |
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Forecasting Integrated and Cointegrated Variables -- Causality Analysis -- Impulse Response Analysis -- 7 . Estimation of Vector Error Correction Models -- Estimation of a Simple Special Case VECM -- Estimation of General VECMs -- LS Estimation -- EGLS Estimation of the Cointegration Parameters -- ML Estimation -- Including Deterministic Terms -- Other Estimation Methods for Cointegrated Systems -- Estimating VECMs with Parameter Restrictions -- Linear Restrictions for the Cointegration Matrix -- Linear Restrictions for the Short-Run and Loading Parameters -- Bayesian Estimation of Integrated Systems -- The Model Setup -- The Minnesota or Litterman Prior -- Forecasting Estimated Integrated and Cointegrated Systems -- Testing for Granger-Causality -- The Noncausality Restrictions -- Problems Related to Standard Wald Tests -- A Wald Test Based on a Lag Augmented VAR -- Impulse Response Analysis -- Algebraic Exercises -- Numerical Exercises -- 8. Specification of VECMs -- Lag Order Selection |
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Testing for the Rank of Cointegration -- A VECM without Deterministic Terms -- A Nonzero Mean Term -- A Linear Trend -- A Linear Trend in the Variables and Not in the Cointegration Relations -- Summary of Results and Other Deterministic Terms -- Prior Adjustment for Deterministic Terms -- Choice of Deterministic Terms -- Other Approaches to Testing for the Cointegrating Rank342 -- Subset VECMs -- Model Diagnostics -- Checking for Residual Autocorrelation -- Testing for Nonnormality -- Tests for Structural Change -- Algebraic Exercises -- Numerical Exercises -- Part III. Structural and Conditional Models -- 9. Structural VARs and VECMs -- Structural Vector Autoregressions -- The A-Model -- The B-Model -- The AB-Model -- Long-Run Restrictions ̀a la Blanchard-Quah -- Structural Vector Error Correction Models -- Estimation of Structural Parameters -- Estimating SVAR Models -- Estimating Structural VECMs -- Impulse Response Analysis and Forecast Error Variance Decomposition -- Further Issues |
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Algebraic Problems -- Numerical Problems -- 10. Systems of Dynamic Simultaneous Equations -- Background -- Systems with Unmodelled Variables -- Types of Variables -- Structural Form, Reduced Form, Final Form -- Models with Rational Expectations -- Cointegrated Variables -- Estimation -- Stationary Variables -- Estimation of Models with I(1) Variables -- Remarks on Model Specification and Model Checking -- Forecasting -- Unconditional and Conditional Forecasts -- Forecasting Estimated Dynamic SEMs -- Multiplier Analysis -- Optimal Control -- Concluding Remarks on Dynamic SEMs -- Part IV. Infinite Order Vector Autoregressive Processes -- 11. Vector Autoregressive Moving Average Processes -- Finite Order Moving Average Processes -- VARMA Processes -- The Pure MA and Pure VAR Representations of a VARMA Process -- A VAR(1) Representation of a VARMA Process -- The Autocovariances and Autocorrelations of a VARMA(p, q) Process -- Forecasting VARMA Processes |
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Transforming and Aggregating VARMA Processes -- Linear Transformations of VARMA Processes -- Aggregation of VARMA Processes -- Interpretation of VARMA Models -- Granger-Causality -- Impulse Response Analysis -- 12. Estimation of VARMA Models -- The Identification Problem -- Nonuniqueness of VARMA Representations -- Final Equations Form and Echelon Form -- Illustrations -- The Gaussian Likelihood Function -- The Likelihood Function of an MA(1) Process -- The MA(q) Case -- The VARMA(1, 1) Case -- The General VARMA(p, q) Case -- Computation of the ML Estimates -- The Normal Equations -- Optimization Algorithms -- The Information Matrix -- Preliminary Estimation -- An Illustration -- Asymptotic Properties of the ML Estimators -- Theoretical Results -- A Real Data Example -- Forecasting Estimated VARMA Processes -- Estimated Impulse Responses -- 13. Specification and Checking the Adequacy of VARMA Models -- Specification of the Final Equations Form -- A Specification Procedure |
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Specification of Echelon Forms -- A Procedure for Small Systems -- A Full Search Procedure Based on Linear Least Squares Computations -- Hannan-Kavalieris Procedure -- Poskitt's Procedure -- Remarks on Other Specification Strategies for VARMA Models -- Model Checking -- LM Tests -- Residual Autocorrelations and Portmanteau Tests -- Prediction Tests for Structural Change -- Critique of VARMA Model Fitting -- 14. Cointegrated VARMA Processes -- The VARMA Framework for I(1) Variables -- Levels VARMA Models -- The Reverse Echelon Form -- The Error Correction Echelon Form -- Estimation -- Estimation of ARMARE Models -- Estimation of EC-ARMARE Models -- Specification of EC-ARMARE Models -- Specification of Kronecker Indices -- Specification of the Cointegrating Rank -- Forecasting Cointegrated VARMA Processes -- Algebraic Exercises -- Numerical Exercises -- 15. Fitting Finite Order VAR Models to Infinite Order Processes -- Background |
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Multivariate Least Squares Estimation -- Forecasting -- Theoretical Results -- Impulse Response Analysis and Forecast Error Variance Decompositions -- Asymptotic Theory -- Cointegrated Infinite Order VARs -- The Model Setup -- Estimation -- Testing for the Cointegrating Rank -- Part V. Time Series Topics -- 16. Multivariate ARCH and GARCH Models -- Background -- Univariate GARCH Models -- Definitions -- Forecasting -- Multivariate GARCH Models -- Multivariate ARCH -- MGARCH -- Other Multivariate ARCH and GARCH Models -- Estimation -- Theory -- Checking MGARCH Models -- ARCH-LM and ARCH-Portmanteau Tests -- LM and Portmanteau Tests for Remaining ARCH -- Other Diagnostic Tests -- Interpreting GARCH Models -- Causality in Variance -- Conditional Moment Profiles and Generalized Impulse Responses -- Problems and Extensions |
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17. Periodic VAR Processes and Intervention Models -- The VAR(p) Model with Time Varying Coefficients -- General Properties -- ML Estimation -- Periodic Processes -- A VAR Representation with Time Invariant Coefficients -- ML Estimation and Testing for Time Varying Coefficients -- Bibliographical Notes and Extensions -- Intervention Models -- Interventions in the Intercept Model -- A Discrete Change in the Mean -- An Illustrative Example -- Extensions and References -- 18. State Space Models -- Background -- State Space Models -- The Model Setup -- More General State Space Models -- The Kalman Filter -- The Kalman Filter Recursions -- Proof of the Kalman Filter Recursions -- Maximum Likelihood Estimation of State Space Models -- The Log-Likelihood Function -- The Identification Problem -- Maximization of the Log-Likelihood Function -- Asymptotic Properties of the ML Estimator |
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A Real Data Example -- Appendices A. Vectors and Matrices -- Basic Definitions -- Basic Matrix Operations -- The Determinant -- The Inverse, the Adjoint, and Generalized Inverses -- Inverse and Adjoint of a Square Matrix -- Generalized Inverses -- The Rank -- Eigenvalues and -vectors -- Characteristic Values and Vectors -- The Trace -- Some Special Matrices and Vectors -- Idempotent and Nilpotent Matrices -- Orthogonal Matrices and Vectors and Orthogonal Complements -- Definite Matrices and Quadratic Forms -- Decomposition and Diagonalization of Matrices -- The Jordan Canonical Form -- Decomposition of Symmetric Matrices -- The Choleski Decomposition of a Positive Definite Matrix -- Partitioned Matrices -- The Kronecker Product -- The vec and vech Operators and Related Matrices -- The Operators -- Elimination, Duplication, and Commutation Matrices -- Vector and Matrix Differentiation |
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Optimization of Vector Functions -- Problems -- B. Multivariate Normal and Related Distributions -- Multivariate Normal Distributions -- Related Distributions -- C. Stochastic Convergence and Asymptotic Distributions -- Concepts of Stochastic Convergence -- Order in Probability -- Infinite Sums of Random Variables -- Laws of Large Numbers and Central Limit Theorems -- Standard Asymptotic Properties of Estimators and Test Statistics -- Maximum Likelihood Estimation -- Likelihood Ratio, Lagrange Multiplier, and Wald Tests -- Unit Root Asymptotics -- Univariate Processes -- Multivariate Processes -- D. Evaluating Properties of Estimators and Test Statistics by Simulation and Resampling Techniques -- Simulating a Multiple Time Series with VAR Generation Process -- Evaluating Distributions of Functions of Multiple Time Series by Simulation -- Resampling Methods |
| Summary |
Deals with analyzing and forecasting multiple time series, considering a range of models and methods. This reference work and graduate-level textbook enables readers to perform their analyses in a competent manner |
| Analysis |
economie |
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economics |
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bedrijfswetenschap |
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management science |
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engineering |
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econometrie |
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econometrics |
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toegepaste wiskunde |
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applied mathematics |
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computational science |
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toegepaste statistiek |
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applied statistics |
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Management studies, Business Administration, Organizational Science (General) |
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Economics (General) |
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Management, bedrijfskunde, organisatiekunde (algemeen) |
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Economie (algemeen) |
| Bibliography |
Includes bibliographical references (pages 713-732)-and indexes |
| Notes |
Print version record |
| Subject |
Time-series analysis.
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MATHEMATICS -- Probability & Statistics -- Time Series.
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Time-series analysis.
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Affaires.
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Science économique.
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Economie de l'entreprise.
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Time-series analysis
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Tijdreeksen.
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Análise de séries temporais.
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| Form |
Electronic book
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| ISBN |
9783540277521 |
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3540277528 |
