# Topics in Dynamic Model Analysis

## Advanced Matrix Methods and Unit-Root Econometrics Representation Theorems

Book

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 558)

1. Front Matter
Pages I-X
2. Pages 53-78
3. Back Matter
Pages 133-146

### Introduction

Classical econometrics - which plunges its roots in economic theory with simultaneous equations models (SEM) as offshoots - and time series econometrics - which stems from economic data with vector autoregr- sive (VAR) models as offsprings - scour, like the Janus's facing heads, the flowing of economic variables so as to bring to the fore their autonomous and non-autonomous dynamics. It is up to the so-called final form of a dy­ namic SEM, on the one hand, and to the so-called representation theorems of (unit-root) VAR models, on the other, to provide informative closed form expressions for the trajectories, or time paths, of the economic vari­ ables of interest. Should we look at the issues just put forward from a mathematical standpoint, the emblematic models of both classical and time series econometrics would turn out to be difference equation systems with ad hoc characteristics, whose solutions are attained via a final form or a represen­ tation theorem approach. The final form solution - algebraic technicalities apart - arises in the wake of classical difference equation theory, display­ ing besides a transitory autonomous component, an exogenous one along with a stochastic nuisance term. This follows from a properly defined ma­ trix function inversion admitting a Taylor expansion in the lag operator be­ cause of the assumptions regarding the roots of a determinant equation pe­ culiar to SEM specifications.

### Keywords

Cointegration Dynamic Econometric Models Matrix Methods for Econometrics Representation Theorems Time series Unit Roots calculus econometrics modeling

#### Authors and affiliations

1. 1.Full Professor of Econometrics and Head of the Department of Econometrics and Applied Mathematics Faculty of EconomicsCatholic University of MilanMilanoItaly
2. 2.Associate Professor of Econometrics Faculty of EconomicsCatholic University of MilanMilanoItaly

### Bibliographic information

• Book Title Topics in Dynamic Model Analysis
• Book Subtitle Advanced Matrix Methods and Unit-Root Econometrics Representation Theorems
• Authors Mario Faliva
Maria Grazia Zoia
• Series Title Lecture Notes in Economics and Mathematical Systems
• DOI https://doi.org/10.1007/3-540-29239-X
• Copyright Information Springer-Verlag Berlin Heidelberg 2006
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages Business and Economics Economics and Finance (R0)
• Softcover ISBN 978-3-540-26196-4
• eBook ISBN 978-3-540-29239-5
• Series ISSN 0075-8442
• Edition Number 1
• Number of Pages X, 144
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site