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Introduction to Multiple Time Series Analysis - Helmut Lutkepohl

Introduction to Multiple Time Series Analysis

Paperback Published: 1st August 1993
ISBN: 9783540569404
Number Of Pages: 545

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This graduate level textbook deals with analyzing and forecasting multiple time series. It considers a wide range of multiple time series models and methods. The models include vector autoregressive, vector autoregressive moving average, cointegrated, and periodic processes as well as state space and dynamic simultaneous equations models. Least squares, maximum likelihood, and Bayesian methods are considered for estimating these models. Different procedures for model selection or specification are treated and a range of tests and criteria for evaluating the adequacy of a chosen model are introduced. The choice of point and interval forecasts is considered and impulse response analysis, dynamic multipliers as well as innovation accounting are presented as tools for structural analysis within the multiple time series context. This book is accessible to graduate students in business and economics. In addition, multiple time series courses in other fields such as statistics and engineering may be based on this book. Applied researchers involved in analyzing multiple time series may benefit from the book as it provides the background and tools for their task. It enables the reader to perform his or her analyses in a gap to the difficult technical literature on the topic.

Introductionp. 1
Objectives of Analyzing Multiple Time Seriesp. 1
Some Basicsp. 2
Vector Autoregressive Processesp. 3
Outline of the Following Chaptersp. 5
Stable Vector Autoregressive Processesp. 9
Basic Assumptions and Properties of VAR Processesp. 9
Forecastingp. 27
Structural Analysis with VAR Modelsp. 35
Estimation of Vector Autoregressive Processesp. 62
Multivariate Least Squares Estimationp. 62
Least Squares Estimation with Mean-Adjusted Data and Yule-Walker Estimationp. 75
Maximum Likelihood Estimationp. 80
Forecasting with Estimated Processesp. 85
Testing for Granger-Causality and Instantaneous Causalityp. 93
The Asymptotic Distributions of Impulse Responses and Forecast Error Variance Decompositionsp. 97
VAR Order Selection and Checking the Model Adequacyp. 118
A Sequence of Tests for Determining the VAR Orderp. 119
Criteria for VAR Order Selectionp. 128
Checking the Whiteness of the Residualsp. 138
Testing for Nonnormalityp. 152
Tests for Structural Changep. 159
VAR Processes with Parameter Constraintsp. 167
Linear Constraintsp. 168
VAR Processes with Nonlinear Parameter Restrictionsp. 192
Bayesian Estimationp. 206
Vector Autoregressive Moving Average Processesp. 217
Finite Order Moving Average Processesp. 217
VARMA Processesp. 220
The Autocovariances and Autocorrelations of a VARMA(p, q) Processp. 226
Forecasting VARMA Processesp. 228
Transforming and Aggregating VARMA Processesp. 230
Interpretation of VARMA Modelsp. 236
Estimation of VARMA Modelsp. 241
The Identification Problemp. 241
The Gaussian Likelihood Functionp. 252
Computation of the ML Estimatesp. 259
Asymptotic Properties of the ML Estimatorsp. 271
Forecasting Estimated VARMA Processesp. 278
Estimated Impulse Responsesp. 281
Specification and Checking the Adequacy of VARMA Modelsp. 284
Specification of the Final Equations Formp. 285
Specification of Echelon Formsp. 289
Remarks on other Specification Strategies for VARMA Modelsp. 297
Model Checkingp. 298
Critique of VARMA Model Fittingp. 302
Fitting Finite Order VAR Models to Infinite Order Processesp. 305
Multivariate Least Squares Estimationp. 305
Forecastingp. 309
Impulse Response Analysis and Forecast Error Variance Decompositionsp. 313
Systems of Dynamic Simultaneous Equationsp. 323
Systems with Exogenous Variablesp. 324
Estimationp. 331
Remarks on Model Specification and Model Checkingp. 333
Forecastingp. 334
Multiplier Analysisp. 338
Optimal Controlp. 339
Concluding Remarks on Dynamic SEMsp. 342
Nonstationary Systems with Integrated and Cointegrated Variablesp. 346
Estimation of Integrated and Cointegrated VAR(p) Processesp. 355
Forecasting and Structural Analysisp. 375
Model Selection and Model Checkingp. 382
Periodic VAR Processes and Intervention Modelsp. 391
The VAR(p) Model with Time Varying Coefficientsp. 392
Periodic Processesp. 396
Intervention Modelsp. 408
State Space Modelsp. 415
State Space Modelsp. 416
The Kalman Filterp. 428
Maximum Likelihood Estimation of State Space Modelsp. 434
A Real Data Examplep. 439
Appendix A. Vectors and Matricesp. 449
Appendix B. Multivariate Normal and Related Distributionsp. 480
Appendix C. Convergence of Sequences of Random Variables and Asymptotic Distributionsp. 484
Appendix D. Evaluating Properties of Estimators and Test Statistics by Simulation and Resampling Techniquesp. 495
Appendix E. Data Used for Examples and Exercisesp. 498
Referencesp. 509
List of Propositions and Definitionsp. 518
Index of Notationp. 521
Author Indexp. 527
Subject Indexp. 531
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540569404
ISBN-10: 3540569405
Audience: General
Format: Paperback
Language: English
Number Of Pages: 545
Published: 1st August 1993
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 24.41 x 16.99  x 2.92
Weight (kg): 0.89
Edition Number: 2
Edition Type: Revised