| Ch. 1 | Introduction | 1 |
| 1.1 | Objectives of Analyzing Multiple Time Series | 1 |
| 1.2 | Some Basics | 2 |
| 1.3 | Vector Autoregressive Processes | 3 |
| 1.4 | Outline of the Following Chapters | 5 |
| Ch. 2 | Stable Vector Autoregressive Processes | 9 |
| 2.1 | Basic Assumptions and Properties of VAR Processes | 9 |
| 2.2 | Forecasting | 27 |
| 2.3 | Structural Analysis with VAR Models | 35 |
| Ch. 3 | Estimation of Vector Autoregressive Processes | 62 |
| 3.2 | Multivariate Least Squares Estimation | 62 |
| 3.3 | Least Squares Estimation with Mean-Adjusted Data and Yule-Walker Estimation | 75 |
| 3.4 | Maximum Likelihood Estimation | 80 |
| 3.5 | Forecasting with Estimated Processes | 85 |
| 3.6 | Testing for Granger-Causality and Instantaneous Causality | 93 |
| 3.7 | The Asymptotic Distributions of Impulse Responses and Forecast Error Variance Decompositions | 97 |
| Ch. 4 | VAR Order Selection and Checking the Model Adequacy | 118 |
| 4.2 | A Sequence of Tests for Determining the VAR Order | 119 |
| 4.3 | Criteria for VAR Order Selection | 128 |
| 4.4 | Checking the Whiteness of the Residuals | 138 |
| 4.5 | Testing for Nonnormality | 152 |
| 4.6 | Tests for Structural Change | 159 |
| Ch. 5 | VAR Processes with Parameter Constraints | 167 |
| 5.2 | Linear Constraints | 168 |
| 5.3 | VAR Processes with Nonlinear Parameter Restrictions | 192 |
| 5.4 | Bayesian Estimation | 206 |
| Ch. 6 | Vector Autoregressive Moving Average Processes | 217 |
| 6.2 | Finite Order Moving Average Processes | 217 |
| 6.3 | VARMA Processes | 220 |
| 6.4 | The Autocovariances and Autocorrelations of a VARMA(p, q) Process | 226 |
| 6.5 | Forecasting VARMA Processes | 228 |
| 6.6 | Transforming and Aggregating VARMA Processes | 230 |
| 6.7 | Interpretation of VARMA Models | 236 |
| Ch. 7 | Estimation of VARMA Models | 241 |
| 7.1 | The Identification Problem | 241 |
| 7.2 | The Gaussian Likelihood Function | 252 |
| 7.3 | Computation of the ML Estimates | 259 |
| 7.4 | Asymptotic Properties of the ML Estimators | 271 |
| 7.5 | Forecasting Estimated VARMA Processes | 278 |
| 7.6 | Estimated Impulse Responses | 281 |
| Ch. 8 | Specification and Checking the Adequacy of VARMA Models | 284 |
| 8.2 | Specification of the Final Equations Form | 285 |
| 8.3 | Specification of Echelon Forms | 289 |
| 8.4 | Remarks on other Specification Strategies for VARMA Models | 297 |
| 8.5 | Model Checking | 298 |
| 8.6 | Critique of VARMA Model Fitting | 302 |
| Ch. 9 | Fitting Finite Order VAR Models to Infinite Order Processes | 305 |
| 9.2 | Multivariate Least Squares Estimation | 305 |
| 9.3 | Forecasting | 309 |
| 9.4 | Impulse Response Analysis and Forecast Error Variance Decompositions | 313 |
| Ch. 10 | Systems of Dynamic Simultaneous Equations | 323 |
| 10.2 | Systems with Exogenous Variables | 324 |
| 10.3 | Estimation | 331 |
| 10.4 | Remarks on Model Specification and Model Checking | 333 |
| 10.5 | Forecasting | 334 |
| 10.6 | Multiplier Analysis | 338 |
| 10.7 | Optimal Control | 339 |
| 10.8 | Concluding Remarks on Dynamic SEMs | 342 |
| Ch. 11 | Nonstationary Systems with Integrated and Cointegrated Variables | 346 |
| 11.2 | Estimation of Integrated and Cointegrated VAR(p) Processes | 355 |
| 11.3 | Forecasting and Structural Analysis | 375 |
| 11.4 | Model Selection and Model Checking | 382 |
| Ch. 12 | Periodic VAR Processes and Intervention Models | 391 |
| 12.2 | The VAR(p) Model with Time Varying Coefficients | 392 |
| 12.3 | Periodic Processes | 396 |
| 12.4 | Intervention Models | 408 |
| Ch. 13 | State Space Models | 415 |
| 13.2 | State Space Models | 416 |
| 13.3 | The Kalman Filter | 428 |
| 13.4 | Maximum Likelihood Estimation of State Space Models | 434 |
| 13.5 | A Real Data Example | 439 |
| Appendix A. Vectors and Matrices | 449 |
| Appendix B. Multivariate Normal and Related Distributions | 480 |
| Appendix C. Convergence of Sequences of Random Variables and Asymptotic Distributions | 484 |
| Appendix D. Evaluating Properties of Estimators and Test Statistics by Simulation and Resampling Techniques | 495 |
| Appendix E. Data Used for Examples and Exercises | 498 |
| References | 509 |
| List of Propositions and Definitions | 518 |
| Index of Notation | 521 |
| Author Index | 527 |
| Subject Index | 531 |
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