Nonlinear Time Series Analysis: Methods And Applications PDF
Preview Nonlinear Time Series Analysis: Methods And Applications
NONLINEAR TIME SERIES ANALYSIS Methods and Applications Cees Difes World Scientific This page is intentionally left blank This page is intentionally left blank This page is intentionally left blank NONLINEAR TIME SERIES ANALYSIS Methods and Applications NONLINEAR TIME SERIES AND CHAOS Editor: Howell Tong Vol. 1: Dimension Estimation and Models ed. H. Tong Vol. 2: Chaos & Forecasting ed. H. Tong Forthcoming Vol. 3: Nonlinear Time Series & Economic Fluctuations S. Potter -; ■ NONLINEAR TIME SERIES ANALYSIS Methods and Applications Cees Diks University of Kent, England World Scientific Singapore • New Jersey • London • Hong Kong Published by World Scientific Publishing Co. Pte. Ltd. P O Box 128, Farrer Road, Singapore 912805 USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Library of Congress Cataloging-in-Publication Data Diks, Cees. Nonlinear time series analysis : methods and applications / Cees Diks. p. cm. -- (Nonlinear time series and chaos : vol. 4) Includes bibliographical references and index. ISBN 9810235054 (alk. paper) 1. Time-senes analysis. 2. Nonlinear theories. I. Title. II. Series. QA280.D55 1999 519.5'5-DC21 99-16722 CIP British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Copyright © 1999 by World Scientific Publishing Co. Pte. Ltd. All rights reserved- This hook, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc , 222 Rosewood Dnve, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. Printed in Singapore by Regal Press (S) Pte Ltd FOREWORD The present volume of Nonlinear Time Series and Chaos gives me the oppor tunity to present a number of methods for the analysis of time series. Although these methods were originally inspired by the need for tools for analyzing the short and noisy nonlinear time series one is often confronted with in physiology, they have since also found several applications in other fields. The currently established methods for the analysis of time series were de veloped mainly in two fields: statistical time series analysis and the theory of dynamical systems. A prolific cross-fertilization has recently started to de velop between these areas, and it is my intention to present some theory and methods in view of this development, indicating the connections between the two fields wherever possible. Statistics has a long tradition of studying joint probability distributions of time series. The analog of this approach in chaos theory is the study of reconstruction measures. As reconstruction measures can be defined both for deterministic time series and stochastic time series they provide a natural framework for a general approach. Throughout, I have tried to keep the material accessible to a readership with an interest in nonlinear time series analysis from a wide variety of research areas; only modest mathematical background knowledge is assumed and exam ples are given throughout to illustrate the ideas behind the methods presented. After a brief introduction to the theory of nonlinear time series analysis, a test for reversibility and a test for comparing two time series are described. Then deterministic time series with observational noise are considered and methods are proposed for estimating the noise level, fractal dimension, and entropy of the dynamics simultaneously. Finally two spatio-temporal dynamical systems are analyzed. I am indebted to Professor H. Tong for offering me the opportunity to write this book and for his encouragement and advice. I thankfully acknowledge Elsevier Science for permission to reproduce Figs 9.2, 9.6 and 9.7 and the American Physical Association for permission to reproduce Figs 6.2, 6.3 and Table 6.1. The work involved research which was partially supported by the Engineering and Physical Sciences Research Council. I gratefully acknowledge Professor W. R. van Zwet, Professor F. Takens and Dr J. DeGoede for their enthusiasm and help in developing much of the material that served as the basis for this book and Qiwei Yao, Catriona Queen and Catarina Resende for their suggestions for improving the manuscript. Canterbury, Fall 1998 Cees Diks v This page is intentionally left blank
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