Introduction to Multiple Time Series Analysis

by Lutkepohl, Helmut

• ISBN13: 9783540569404
• ISBN10: 3540569405
• Edition: 2nd
• Format: Paperback
• Copyright: 1993-08-01
• Publisher: Springer Verlag

Summary

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.

Table of Contents

Introduction	p. 1
Objectives of Analyzing Multiple Time Series	p. 1
Some Basics	p. 2
Vector Autoregressive Processes	p. 3
Outline of the Following Chapters	p. 5
Stable Vector Autoregressive Processes	p. 9
Basic Assumptions and Properties of VAR Processes	p. 9
Forecasting	p. 27
Structural Analysis with VAR Models	p. 35
Estimation of Vector Autoregressive Processes	p. 62
Multivariate Least Squares Estimation	p. 62
Least Squares Estimation with Mean-Adjusted Data and Yule-Walker Estimation	p. 75
Maximum Likelihood Estimation	p. 80
Forecasting with Estimated Processes	p. 85
Testing for Granger-Causality and Instantaneous Causality	p. 93
The Asymptotic Distributions of Impulse Responses and Forecast Error Variance Decompositions	p. 97
VAR Order Selection and Checking the Model Adequacy	p. 118
A Sequence of Tests for Determining the VAR Order	p. 119
Criteria for VAR Order Selection	p. 128
Checking the Whiteness of the Residuals	p. 138
Testing for Nonnormality	p. 152
Tests for Structural Change	p. 159
VAR Processes with Parameter Constraints	p. 167
Linear Constraints	p. 168
VAR Processes with Nonlinear Parameter Restrictions	p. 192
Bayesian Estimation	p. 206
Vector Autoregressive Moving Average Processes	p. 217
Finite Order Moving Average Processes	p. 217
VARMA Processes	p. 220
The Autocovariances and Autocorrelations of a VARMA(p, q) Process	p. 226
Forecasting VARMA Processes	p. 228
Transforming and Aggregating VARMA Processes	p. 230
Interpretation of VARMA Models	p. 236
Estimation of VARMA Models	p. 241
The Identification Problem	p. 241
The Gaussian Likelihood Function	p. 252
Computation of the ML Estimates	p. 259
Asymptotic Properties of the ML Estimators	p. 271
Forecasting Estimated VARMA Processes	p. 278
Estimated Impulse Responses	p. 281
Specification and Checking the Adequacy of VARMA Models	p. 284
Specification of the Final Equations Form	p. 285
Specification of Echelon Forms	p. 289
Remarks on other Specification Strategies for VARMA Models	p. 297
Model Checking	p. 298
Critique of VARMA Model Fitting	p. 302
Fitting Finite Order VAR Models to Infinite Order Processes	p. 305
Multivariate Least Squares Estimation	p. 305
Forecasting	p. 309
Impulse Response Analysis and Forecast Error Variance Decompositions	p. 313
Systems of Dynamic Simultaneous Equations	p. 323
Systems with Exogenous Variables	p. 324
Estimation	p. 331
Remarks on Model Specification and Model Checking	p. 333
Forecasting	p. 334
Multiplier Analysis	p. 338
Optimal Control	p. 339
Concluding Remarks on Dynamic SEMs	p. 342
Nonstationary Systems with Integrated and Cointegrated Variables	p. 346
Estimation of Integrated and Cointegrated VAR(p) Processes	p. 355
Forecasting and Structural Analysis	p. 375
Model Selection and Model Checking	p. 382
Periodic VAR Processes and Intervention Models	p. 391
The VAR(p) Model with Time Varying Coefficients	p. 392
Periodic Processes	p. 396
Intervention Models	p. 408
State Space Models	p. 415
State Space Models	p. 416
The Kalman Filter	p. 428
Maximum Likelihood Estimation of State Space Models	p. 434
A Real Data Example	p. 439
Appendix A. Vectors and Matrices	p. 449
Appendix B. Multivariate Normal and Related Distributions	p. 480
Appendix C. Convergence of Sequences of Random Variables and Asymptotic Distributions	p. 484
Appendix D. Evaluating Properties of Estimators and Test Statistics by Simulation and Resampling Techniques	p. 495
Appendix E. Data Used for Examples and Exercises	p. 498
References	p. 509
List of Propositions and Definitions	p. 518
Index of Notation	p. 521
Author Index	p. 527
Subject Index	p. 531
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