A Nonlinear Time Series Workshop A Toolkit for Detecting and Identif
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Dynamic Modeling and Econometrics in Economics and Finance
VOLUME 2
Series Editors Stefan Mittnik, University of Kiel, Germany Willi Semmler, University of Bielefeld, Germany and New School for Sacul! Research, USA
A NONLINEAR TIME SERIES WORKSHOP: A Toolkit for Detecting and Identifying Nonlinear Serial Dependence
by Douglas M. Patterson Department of Finance, Insurance, and Business Law Virginia Polytechnic Institute and State University Blacksburg, Virginia Richard A. Ashley Department of Economics Virginia Polytechnic Institute ofTechnology Blacksburg, Virginia
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library of Congress Cataloging-in-Publication Data Patterson,Douglas M.(Douglas MacLennan),1945A nonlinear time series workshop : a toolkit for detecting and identifying nonlinear serial dependence I by Douglas M.Patterson, Richard A.Ashley. p.cm.-- (Dynamic modeling and econometrics in economics and finance; v.2) Includes bibliographical references and index. ISBN 978-1-4613-4665-4 ISBN 978-1-4419-8688-7 (eBook) DOI 10.1007/978-1-4419-8688-7 1. Time-series analysis--Congresses.2.Economics,Mathematical-Congresses. I.Ashley,Richard A.(Richard Arthur),1950-II. Title.ill.Series. HA30.3 .P38 1999 99-046691 330' .0I'519232-dc21
Copyright ~ 2000 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2000 Softcover reprint of the hardcover 1st edition 2000 AH rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photo-copying, recording, or otherwise, without the prior written permis sion of the publisher, Springer Science+Business Media, LLC
Printed on acid-free paper.
Table of Contents
Preface 1. Nonlinearity in Stochastic Processes: What it Is and Why it Matters
VB
1
2. Detecting Nonlinear Serial Dependence
39
3. How to Run the Toolkit Program on a PC
51
4. Artificially Generated Data: Size Considerations
63
5. Artificially Generated Data: Power And Model Specification Considerations
73
6. Analysis of Stock Market Returns
95
7. Glint Tracking Errors in Radar
121
8. Seismic Data
137
9. Analysis of U.S. Real GNP
161
10. Dynamic Structure of Macroeconomic Technology Shocks
167
11. Climatological Data
177
Index
189
Preface The analysis of what might be called "dynamic nonlinearity" in time series has its roots in the pioneering work of Brillinger (1965) - who first pointed out how the bispectrum and higher order polyspectra could, in principle, be used to test for nonlinear serial dependence - and in Subba Rao and Gabr (1980) and Hinich (1982) who each showed how Brillinger's insight could be translated into a statistical test. Hinich's test, because it takes advantage ofthe large sample statistical properties ofthe bispectral estimates became the first usable statistical test for nonlinear serial dependence. We are forever grateful to Mel Hinich for getting us involved at that time in this fascinating and fruitful endeavor. With help from Mel (someti
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