Recent Developments in Nonlinear Cointegration with Applications to Macroeconomics and Finance
This book is an introductory exposition of different topics that emerged in the literature as unifying themes between two fields of econometrics of time series, namely nonlinearity and nonstationarity. Papers on these topics have exploded over the last tw
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Recent Developments in Nonlinear Cointegration with Applications to Macroeconomics and Finance by
Gilles Dufrenot ERUDITE, University of Paris 12 and GREQUAM-CNRS, University of Marseille, France
and
Valerie Mignon MODEM, University of Paris 10, France
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-1-4419-5276-9 ISBN 978-1-4757-3615-1 (eBook) DOI 10.1007/978-1-4757-3615-1
Printed on acid-free paper
AlI Rights Reserved © 2002 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2002 Softcover reprint of the hardcover 1st edition 2002 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permis sion from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.
This book is dedicated to Tania, Marc-Aurele and Pierre-Andre
Contents
List of Figures List of Tables Preface Acknowledgments
IX XXI
xxiii xxvii
1. INTRODUCTION 1
2
3
1
Combining the hypotheses of nonstationarity and nonlinearity 1.1 The economic arguments The econometric arguments 1.2 1.3 Terminology and methodological aspects 1.4 An overview of the main topics of the book A brief review of some nonlinear models Bilinear models 2.1 2.2 Threshold autoregressive models Unit root and stationarity tests The Dickey-Fuller tests 3.1 The Phillips-Perron tests 3.2 3.3 The Schmidt-Phillips test The Elliott, Rothenberg and Stock test 3.4 3.5 The KPSS test
1
1 3 6 8 11 11
19 26 26 31 33 35 38
2. ARE THE UNIT-ROOT TESTS ADEQUATE FOR NONLINEAR 45 MODELS? 1
Introduction
45
2
Examples of nonlinear models with unit roots and longmemory 2.1 The squared transformation of a unit root process
47 47
v
NONLINEAR COINTEGRATION
VI
2.2 2.3 2.4 2.5 2.6
SETAR(2,1,1) models with unit roots SETAR models with interior regimes Other nonlinear processes Long-range dependerit nonlinear models Hermite expansion of nonlinearly transformed 1(1) processes
48 49 51 52 54
3
Monte Carlo experiments: applying the classical tests to nonlinear models 58 3.1 Smooth transition models 59 3.2 Bilinear models 62 3.3 Other nonlinear time series models 68 3.4 Monte Carlo simulations on nonlinear transformations of unit roots 70
4
Extensions of traditional unit root tests based on ADF regressions 4.1 ADF tests based on the rank of the series 4.2 A modified ADF test based on Taylor expansions
5
Nonlinear stochastic and deterministic trends 75 5.1 Introducing hysteresis in random walks models 75 5.2 Detecting nonlinear stochastic trends in macroeconomic series 79 Data analysis on macroeconomic and financial variables 80 Unit root tests on bilinear models: the example of 6.1 financial "data 80 Applying MADF regressions on macroeconomic 6.2 86 time series Are there nonl
