This monograph provides an insightful analysis of dynamic modelling in econometrics by bridging the structural with the time series approaches, and by focusing on representation theorems of integrated processes. The book provides mainly a self-contained, rigorous as well as innovative, analytic setting to guide formulation and solution in closed form of vector autoregressive (VAR) models with unit roots. The second edition implements the latest research work by the second author on linear matrix polynomials whence a further breakthought on the topic is gained. Its emphasis is placed on representation theorems, conjugating an elegant reappraisal of classical results with original insights which widen their information content. A unified representation theorem of new conception is established, which duly shapes the contours of the cointegration features of VAR solutions, providing not only a contribution to clarity but also new stimuli in this fascinating field of research as a spin-off.
Author(s): Mario Faliva, Maria Grazia Zoia
Edition: 2nd ed.
Publisher: Springer
Year: 2010
Language: English
Pages: 225
Tags: Финансово-экономические дисциплины;Эконометрика;
3540859950......Page 1
Contents......Page 5
Preface to the Second Edition......Page 7
Preface to the First Edition......Page 8
1.1 Generalized Inverses......Page 10
1.2 Orthogonal Complements......Page 15
1.3 Empty Matrices......Page 27
1.4 Partitioned Inversion: Classic and Newly Found Results......Page 28
1.5 Useful Matrix Decompositions......Page 39
1.6 Matrix Polynomial Functions: Zeroes, Roots and Poles......Page 47
1.7 The Laurent Form of a Matrix-Polynomial Inverse about a Unit-Root......Page 60
1.8 Matrix Polynomials and Difference Equation Systems......Page 71
1.9 The Linear Matrix Polynomial......Page 83
1.10 Index and Rank Properties of Matrix Coefficients vs. Pole Order in Matrix Polynomial Inversion......Page 93
1.11 Closed-Forms of Laurent Expansion Coefficient Matrices. First Approach......Page 106
1.12 Closed-Forms of Laurent Expansion Coefficient Matrices. Second Approach......Page 120
2.1 Stochastic Processes: Preliminaries......Page 135
2.2 Principal Multivariate Stationary Processes......Page 138
2.3 The Source of Integration and the Seeds of Cointegration......Page 150
2.4 Integrated and Cointegrated Processes......Page 153
2.5 Casting a Glance at the Backstage of VAR Modelling......Page 159
Appendix A: Convenient Reparametrization of a VAR Model and Related Results......Page 163
Appendix B: Integrated Processes, Stochastic Trends and Rôle of Cointegration......Page 167
3.1 Macroeconometric Structural Models versus VAR Models......Page 169
3.2 Basic VAR Specifications and Engendered Processes......Page 175
3.3 A Sequential Rank Criterion for the Integration Order of a VAR Solution......Page 180
3.4 Representation Theorems for Processes I (1)......Page 187
3.5 Representation Theorems for Processes I (2)......Page 197
3.6 A Unified Representation Theorem......Page 211
References......Page 220
Notational Conventions, Symbols and Acronyms......Page 222
List of Definitions......Page 224
