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NONLINEAR TIME SERIES ANALYSIS
This book reprents a modern approach to time ries analysis which is bad on
the theory of dynamical systems.It starts from a sound outline of the underlying
theory to arrive at very practical issues,which are illustrated using a large number of
empirical data ts taken from variousfields.This book will hence be highly uful
for scientists and engineers from all disciplines who study time variable signals,
including the earth,life and social sciences.
The paradigm of deterministic chaos has influenced thinking in manyfields of
science.Chaotic systems show rich and surprising mathematical structures.In the
applied sciences,deterministic chaos provides a striking explanation for irregular
temporal behaviour and anomalies in systems which do not em to be inherently
stochastic.The most direct link between chaos theory and the real world is the anal-
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ysis of time ries from real systems in terms of nonlinear dynamics.Experimental
technique and data analysis have en such dramatic progress that,by now,most
fundamental properties of nonlinear dynamical systems have been obrved in the
laboratory.Great efforts are being made to exploit ideas from chaos theory where-
ver the data display more structure than can be captured by traditional methods.
Problems of this kind are typical in biology and physiology but also in geophysics,
economics and many other sciences.
This revid edition has been significantly rewritten an expanded,including
veral new chapters.In view of applications,the most relevant novelties will be the
treatment of non-stationary data ts and of nonlinear stochastic process inside
the framework of a state space reconstruction by the method of delays.Hence,non-
linear time ries analysis has left the rather narrow niche of strictly deterministic
systems.Moreover,the analysis of multivariate data ts has gained more atten-
tion.For a direct application of the methods of this book to the reader’s own data
ts,this book cloly refers to the publicly available software package TISEAN.
The availability of this software will facilitate the solution of the exercis,so that
readers now can easily gain their own experience with the analysis of data ts.
Holger Kantz,born in November1960,received his diploma in physics from
含蓄美the University of Wuppertal in January1986with a thesis on transient chaos.In
January1989he obtained his Ph.D.in theoretical physics from the same place,
having worked under the supervision of Peter Grassberger on Hamiltonian many-
particle dynamics.During his postdoctoral time,he spent one year on a Marie Curie
fellowship of the European Union at the physics department of the University of
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Florence in Italy.In January1995he took up an appointment at the newly founded
Max Planck Institute for the Physics of Complex Systems in Dresden,where he
established the rearch group‘Nonlinear Dynamics and Time Series Analysis’.
In1996he received his venia legendi and in2002he became adjunct professor
in theoretical physics at Wuppertal University.In addition to time ries analysis,
he works on low-and high-dimensional nonlinear dynamics and its applications.
More recently,he has been trying to bridge the gap between dynamics and statis-
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tical physics.He has(co-)authored more than75peer-reviewed articles in scien-
tific journals and holds two international patents.For up-to-date information e
www.mpipks-dresden.mpg.de/mpi-doc/kantzgruppe.html.
Thomas Schreiber,born1963,did his diploma work with Peter Grassberger at
俄罗斯节假日Wuppertal University on pha transitions and information transport in spatio-
temporal chaos.He joined the chaos group of Predrag Cvitanovi´c at the Niels Bohr
Institute in Copenhagen to study periodic orbit theory of diffusion and anomalous
transport.There he also developed a strong interest in real-world applications of
chaos theory,leading to his Ph.D.thesis on nonlinear time ries analysis(Univer-
sity of Wuppertal,1994).As a rearch assistant at Wuppertal University and during
veral extended appointments at the Max Planck Institute for the Physics of Com-
plex Systems in Dresden he published numerous rearch articles on time ries
methods and applications ranging from physiology to the stock market.His habil-
itation thesis(University of Wuppertal)appeared as a review in Physics Reports
in1999.Thomas Schreiber has extensive experience teaching nonlinear dynamics
to students and experts from variousfields and at all levels.Recently,he has left
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academia to undertake industrial rearch.
马蹄粉的功效与作用
NONLINEAR TIME SERIES ANALYSIS HOLGER KANTZ AND THOMAS SCHREIBER
Max Planck Institute for the Physics of Complex Systems,
Dresden
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published by the press syndicate of the university of cambridge
The Pitt Building,Trumpington Street,Cambridge,United Kingdom
cambridge university press
The Edinburgh Building,Cambridge CB22RU,UK
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www.cambridge
C Holger Kantz and Thomas Schreiber,2000,2003
This book is in copyright.Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.
First published2000
Second edition published2003
东北师大Printed in the United Kingdom at the University Press,Cambridge
Typeface Times11/14pt.System L A T E X2ε[tb]
A catalogue record for this book is available from the British Library
Library of Congress Cataloguing in Publication data
Kantz,Holger,1960–
Nonlinear time ries analysis/Holger Kantz and Thomas Schreiber.–[2nd ed.].
<
Includes bibliographical references and index.
ISBN0521821509–ISBN0521529026(paperback)
1.Time-ries analysis.
2.Nonlinear theories.I.Schreiber,Thomas,1963–II.Title
QA280.K3552003
519.5 5–dc212003044031
ISBN0521821509hardback
ISBN0521529026paperback
The publisher has ud its best endeavours to ensure that the URLs for external websites referred to in this book
are correct and active at the time of going to press.However,the publisher has no responsibility for the websites and can make no guarantee that a site will remain live or that the content is or will remain appropriate.
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Contents
Preface to thefirst edition page xi
Preface to the cond edition xiii
Acknowledgements xv生理周期表
I Basic topics1
1Introduction:why nonlinear methods?3
2Linear tools and general considerations13
2.1Stationarity and sampling13
2.2Testing for stationarity15
2.3Linear correlations and the power spectrum18
2.3.1Stationarity and the low-frequency component in the
power spectrum23
2.4Linearfilters24
2.5Linear predictions27
3Pha space methods30
3.1Determinism:uniqueness in pha space30
3.2Delay reconstruction35
3.3Finding a good embedding36
3.3.1Fal neighbours37
3.3.2The time lag39
3.4Visual inspection of data39
3.5Poincar´e surface of ction41
3.6Recurrence plots43
4Determinism and predictability48
4.1Sources of predictability48
4.2Simple nonlinear prediction algorithm50
4.3Verification of successful prediction53
4.4Cross-prediction errors:probing stationarity56
4.5Simple nonlinear noi reduction58
v
