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1、ThispageintentionallyleftblankNONLINEARTIMESERIESANALYSISThisbookrepresentsamodernapproachtotimeseriesanalysiswhichisbasedonthetheoryofdynamicalsystems.Itstartsfromasoundoutlineoftheunderlyingtheorytoarriveatverypracticalissues,whichareillustratedusingalargenumberofempiricaldatasetstakenfrom
2、various?elds.Thisbookwillhencebehighlyusefulforscientistsandengineersfromalldisciplineswhostudytimevariablesignals,includingtheearth,lifeandsocialsciences.Theparadigmofdeterministicchaoshasin?uencedthinkinginmany?eldsofscience.Chaoticsystemsshowrichandsurprisingmathematicalstructures.Intheap
3、pliedsciences,deterministicchaosprovidesastrikingexplanationforirregulartemporalbehaviourandanomaliesinsystemswhichdonotseemtobeinherentlystochastic.Themostdirectlinkbetweenchaostheoryandtherealworldistheanal-ysisoftimeseriesfromrealsystemsintermsofnonlineardynamics.Experimentaltechniqueandd
4、ataanalysishaveseensuchdramaticprogressthat,bynow,mostfundamentalpropertiesofnonlineardynamicalsystemshavebeenobservedinthelaboratory.Greateffortsarebeingmadetoexploitideasfromchaostheorywhere-verthedatadisplaymorestructurethancanbecapturedbytraditionalmethods.Problemsofthiskindaretypicalinb
5、iologyandphysiologybutalsoingeophysics,economicsandmanyothersciences.Thisrevisededitionhasbeensigni?cantlyrewrittenanexpanded,includingseveralnewchapters.Inviewofapplications,themostrelevantnoveltieswillbethetreatmentofnon-stationarydatasetsandofnonlinearstochasticprocessesinsidetheframework
6、ofastatespacereconstructionbythemethodofdelays.Hence,non-lineartimeseriesanalysishaslefttherathernarrownicheofstrictlydeterministicsystems.Moreover,theanalysisofmultivariatedatasetshasgainedmoreatten-tion.Foradirectapplicationofthemethodsofthisbooktothereader’sowndatasets,thisbookcloselyrefe
7、rstothepubliclyavailablesoftwarepackageTISEAN.Theavailabilityofthissoftwarewillfacilitatethesolutionoftheexercises,sothatreadersnowcaneasilygaintheirownexperiencewiththeanalysisofdatasets.HolgerKantz,borninNovember1960,receivedhisdiplomainphysicsfr
