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

by Faliva, Mario; Zoia, Maria Grazia

• ISBN13: 9783540261964
• ISBN10: 3540261966
• Format: Paperback
• Copyright: 2005-12-05
• Publisher: Springer Verlag

Summary

This monograph provides an insightful analysis of dynamic modelling in econometrics by bridging the unit-root gap between structural and time series approaches and focusing on representation theorems of (co)integrated processes.The book starts by providing a self-contained ' rigorous al well as innovative ' analytical setting to guide the formulation and solution in closed form of vector autoregressive models with unit roots. The monograph then moves on to place emphasis on the so-called representation theorems of unit-root econometrics, conjugating an elegant reappraisal of classical results with original enlightening insights which widen and enrich the information content and meaning of the said theorems, therefore providing new stimuli in this fascinating field of research.

Table of Contents

Preface	vii
The Algebraic Framework of Unit-Root Econometrics	1	(52)
Generalized Inverses and Orthogonal Complements	1	(9)
Partitioned Inversion: Classical and Newly Found Results	10	(6)
Matrix Polynomials: Preliminaries	16	(3)
Matrix Polynomial Inversion by Laurent Expansion	19	(5)
Matrix Polynomials and Difference Equation Systems	24	(6)
Matrix Coefficient Rank Properties vs. Pole Order in Matrix Polynomial Inversion	30	(7)
Closed-Forms of Laurent Expansion Coefficient Matrices	37	(16)
The Statistical Setting	53	(26)
Stochastic Processes: Preliminaries	53	(3)
Principal Multivariate Stationary Processes	56	(12)
The Source of Integration and the Seeds of Cointegration	68	(3)
A Glance at Integrated and Cointegrated Processes	71	(8)
Appendix. Integrated Processes, Stochastic Trends and Role of Cointegration	77	(2)
Econometric Dynamic Models: from Classical Econometrics to Time Series Econometrics	79	(54)
Macroeconometric Structural Models Versus VAR Models	79	(6)
Basic VAR Specifications and Engendered Processes	85	(5)
A Sequential Rank Criterion for the Integration Order of a VAR Solution	90	(7)
Representation Theorems for Processes I (1)	97	(13)
Representation Theorems for Processes I (2)	110	(18)
A Unified Representation Theorem	128	(5)
Appendix. Empty Matrices	131	(2)
References	133	(4)
Notational Conventions, Symbols and Acronyms	137	(2)
List of Definitions	139	(2)
List of Theorems, Corollaries and Propositions	141