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Mario Faliva
Maria Grazia Zoia
Topics in Dynamic
Model Analysis
Advanced Matrix Methods and Unit-Root
Econometrics Representation Theorems
Springer 2005
Contents
Preface VII
1 The Algebraic Framework of Unit-Root Econometrics 1
1.1 Generalized Inverses and Orthogonal Complements 1
1.2 Partitioned Inversion: Classical and Newly Found Results , 10
1.3 Matrix Polynomials: Preliminaries....... 16
1.4 Matrix Polynomial Inversion by Laurent Expansion 19
1.5 Matrix Polynomials and Difference Equation Systems... .24
1.6 Matrix Coefficient Rank Properties vs. Pole Order in Matrix
Polynomial Inversion 30
1.7 Closed-Forms of Laurent Expansion Coefficient Matrices 37
2 The Statistical Setting 53
2.1 Stochastic Processes: Prehminaries .........53
2.2 Principal Multivariate Stationary Processes ...56
2.3 The Source of Integration and the Seeds of Cointegration.. 68
2.4 A Glance at Integrated and Cointegrated Processes 71
Appendix. Integrated Processes, Stochastic Trends and Role
of Cointegration 77
3 Econometric Dynamic Models: from Classical Econometrics
to Time Series Econometrics 79
3.1 Macroeconometric Structural Models Versus VAR Models 79
3.2 Basic VAR Specifications and Engendered Processes ..85
3.3 A Sequential Rank Criterion for the Integration Order of a VAR
Solution. 90
3.4 Representation Theorems for Processes /(I) ...97
3.5 Representation Theorems for Processes / (2) 110
3.6 A Unified Representation Theorem.... 128
Appendix. Empty Matrices.... 131
References 133
Notational Conventions, Symbols and Acronyms 137
X Contents
List of Definitions 139
List of Theorems, Corollaries and Propositions 141
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