Dynamic model analysis : advanced matrix methods and unit-root econometrics representation theorems / Mario Faliva, Maria Grazia Zoia.

Format:

Book

Author/Creator:

Faliva, Mario.

Contributor:

Zoia, Maria Grazia.

Language:

English

Subjects (All):

Econometrics--Mathematical models.

Econometrics.

Physical Description:

x, 218 pages : illustrations ; 24 cm

Edition:

Second edition.

Place of Publication:

Berlin : Springer, 2009.

Summary:

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.

Contents:

1 The Algebraic Framework of Unit- Root Econometrics 1

1.1 Generalized Inverses 1

1.2 Orthogonal Complements 6

1.3 Empty Matrices 18

1.4 Partitioned Inversion: Classic and Newly Found Results 19

1.5 Useful Matrix Decompositions 30

1.6 Matrix Polynomial Functions: Zeroes, Roots and Poles 38

1.7 The Laurent Form of a Matrix-Polynomial Inverse about a Unit-Root 51

1.8 Matrix Polynomials and Difference Equation Systems 62

1.9 The Linear Matrix Polynomial 74

1.10 Index and Rank Properties of Matrix Coefficients vs. Pole Order in Matrix Polynomial Inversion 84

1.11 Closed-Forms of Laurent Expansion Coefficient Matrices. First Approach 97

1.12 Closed-Forms of Laurent Expansion Coefficient Matrices. Second Approach 111

2 The Statistical Setting 127

2.1 Stochastic Processes: Preliminaries 127

2.2 Principal Multivariate Stationary Processes 130

2.3 The Source of Integration and the Seeds of Cointegration 142

2.4 Integrated and Cointegrated Processes 145

2.5 Casting a Glance at the Backstage of VAR Modelling 151

Appendix A Convenient Reparametrization of a VAR Model and Related Results 155

Appendix B Integrated Processes, Stochastic Trends and Role of Cointegration 159

3 Econometric Dynamic Models: from Classical Econometrics to Time Series Econometrics 161

3.1 Macroeconometric Structural Models versus VAR Models 161

3.2 Basic VAR Specifications and Engendered Processes 167

3.3 A Sequential Rank Criterion for the Integration Order of a VAR Solution 172

3.4 Representation Theorems for Processes I (1) 179

3.5 Representation Theorems for Processes I (2) 189

3.6 A Unified Representation Theorem 203.

Notes:

Includes bibliographical references.

ISBN:

3540859950

9783540859956

OCLC:

268931901