Dynamic Model Analysis: Advanced Matrix Methods and Unit-Root Econometrics Representation Theorems

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Springer Science & Business Media, Oct 24, 2008 - Business & Economics - 218 pages
This second edition sees the light three years after the first one: too short a time to feel seriously concerned to redesign the entire book, but sufficient to be challenged by the prospect of sharpening our investigation on the working of econometric dynamic models and to be inclined to change the title of the new edition by dropping the “Topics in” of the former edition. After considerable soul searching we agreed to include several results related to topics already covered, as well as additional sections devoted to new and sophisticated techniques, which hinge mostly on the latest research work on linear matrix polynomials by the second author. This explains the growth of chapter one and the deeper insight into representation theorems in the last chapter of the book. The rôle of the second chapter is that of providing a bridge between the mathematical techniques in the backstage and the econometric profiles in the forefront of dynamic modelling. For this purpose, we decided to add a new section where the reader can find the stochastic rationale of vector autoregressive specifications in econometrics. The third (and last) chapter improves on that of the first edition by re- ing the fruits of the thorough analytic equipment previously drawn up.
 

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Contents

The Algebraic Framework of UnitRoot Econometrics
1
12 Orthogonal Complements
6
13 Empty Matrices
18
Classic and Newly Found Results
19
15 Useful Matrix Decompositions
30
Zeroes Roots and poles
38
17 The Laurent Form of a MatrixPolynomial Inverse about a UnitRoot
51
18 Matrix Polynomials and Difference Equation Systems
62
24 Integrated and Cointegrated Processes
145
25 Casting a Glance at the Backstage of VAR Modelling
151
A Convenient Reparametrization of a VAR Model and Related Results
155
Integrated Processes Stochastic Trends and Role of Cointegration
159
Econometric Dynamic Models From Classical Econometrics to Time Series Econometrics
161
32 Basic VAR Specifications and Engendered Processes
167
33 A Sequential Rank Criterion for the Integration Order of a VAR Solution
172
34 Representation Theorems for Processes I 1
179

19 The Linear Matrix Polynomial
74
110 Index and Rank Properties of Matrix Coefficients vs Pole Order in Matrix Polynomial Inversion
84
111 ClosedForms of Laurent Expansion Coefficient Matrices First Approach
97
112 ClosedForms of Laurent Expansion Coefficient Matrices Second Approach
111
The Statistical Setting
127
22 Principal Multivariate Stationary Processes
130
23 The Source of Integration and the Seeds of Cointegration
142
35 Representation Theorems for Processes 2
189
36 A Unified Representation Theorem
203
References
212
Notational Conventions Symbols and Acronyms
215
List of Definitions
217
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