Dynamic Model Analysis Advanced Matrix Methods and Unit-Root Econome
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,
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Mario Faliva Maria Grazia Zoia ●
Dynamic Model Analysis Advanced Matrix Methods and Unit-Root Econometrics Representation Theorems Second Edition
Professor Mario Faliva Professor Maria Grazia Zoia Catholic University of Milan Faculty of Economics Department of Mathematics and Econometrics Largo Gemelli, 1 20123 Milano Italy [email protected] [email protected]
ISBN 978-3-540-85995-6
e-ISBN 978-3-540-85996-3
Library of Congress Control Number: 2008934857 © 2006, 2009 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permissions for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg, Germany Printed on acid-free paper 987654321 springer.com
Contents
Preface to the Second Edition…………………………………………………. vii Preface to the First Edition………………………………………………….….. ix 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
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