61Chapter13__Handbook of Time Series Analysis

HandbookofTimeSeriesAnalysisEditedbyBjörnSchelter,MathiasWinterhalder,andJensTimmerRelatedTitlesKedem,B.,Fokianos,K.RegressionModelsforTimeSeriesAnalysis360pages2002HardcoverISBN-13:978-0-471-36355-2ISBN-10:0-471-36355-3Pourahmadi,MFoundationsofTimeSeriesAnalysisandPredictionTheory448pages2001HardcoverISBN-13:978-0-471-39434-1ISBN-10:0-471-39434-3Pena,DACourseinTimeSeriesAnalysis496pages2000HardcoverISBN-13:978-0-471-36164-0ISBN-10:0-471-36164-XHandbookofTimeSeriesAnalysisRecentTheoreticalDevelopmentsandApplicationsEditedbyBjörnSchelter,MatthiasWinterhalder,andJensTimmerWILEY-VCHVerlagGmbH&Co.KGaATheEditorsBjörnSchelterUniversityofFreiburgCenterforDataAnalysisEckerstr.179104FreiburgMatthiasWinterhalderFreiburgerZentrumfürDatenanalyseundModellbildung-FDMEckerstr.179104FreiburgJensTimmerAlbert-Ludwig-Univ.FreiburgZentrumf.Datenanalyse(FDM)Eckerstr.179104FreiburgAllbookspublishedbyWiley-VCHarecarefullyproduced.Nevertheless,authors,editors,andpublisherdonotwarranttheinformationcontainedinthesebooks,includingthisbook,tobefreeoferrors.Readersareadvisedtokeepinmindthatstatements,data,illustrations,proceduraldetailsorotheritemsmayinadvertentlybeinaccurate.LibraryofCongressCardNo.:appliedforBritishLibraryCataloguing-in-PublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary.BibliographicinformationpublishedbyDieDeutscheBibliothekDieDeutscheBibliothekliststhispublicationintheDeutscheNationalbibliografie;detailedbibliographicdataisavailableintheInternetat©2006WILEY-VCHVerlagGmbH&Co.KGaA,WeinheimAllrightsreserved(includingthoseoftranslationintootherlanguages).Nopartofthisbookmaybereproducedinanyform–photoprinting,microfilm,oranyothermeans–transmittedortranslatedintoamachinelanguagewithoutwrittenpermissionfromthepublishers.Registerednames,trademarks,etc.usedinthisbook,evenwhennotspecificallymarkedassuch,arenottobeconsideredunprotectedbylaw.TypesettingDa-TeXGerdBlumenstein,LeipzigBindingLitges&DopfGmbH,HeppenheimCoverDesignaktivCommGmbH,WeinheimPrintedintheFederalRepublicofGermanyPrintedonacid-freepaperISBN-13:978-3-527-40623-4ISBN-10:3-527-40623-9ContentsPrefacexiiiListofContributorsxv1HandbookofTimeSeriesAnalysis:IntroductionandOverview(BjörnSchelter,MatthiasWinterhalder,andJensTimmer)12NonlinearAnalysisofTimeSeriesData(HenryD.I.AbarbanelandUlrichParlitz)52.1Introduction................................52.2UnfoldingtheData:EmbeddingTheoreminPractice........62.2.1ChoosingT:AverageMutualInformation...........82.2.2ChoosingD:FalseNearestNeighbors.............132.2.3InterspikeIntervals........................182.3WhereareWe?..............................182.4LyapunovExponents:Prediction,Classification,andChaos....192.5Predicting.................................242.6Modeling..................................282.6.1ModelingInterspikeIntervals..................282.6.2ModelingtheObservedMembraneVoltageTimeSeries..292.6.3ODEModeling..........................332.7Conclusion.................................33References....................................353LocalandClusterWeightedModelingforTimeSeriesPrediction(DavidEngsterandUlrichParlitz)393.1Introduction................................393.1.1TimeSeriesPrediction......................403.1.2CrossPrediction.........................403.1.3Bias,Variance,Overfitting....................413.2LocalModeling..............................423.2.1Validation.............................433.2.2LocalPolynomialModels....................453.2.3LocalAveragingModels.....................463.2.4LocallyLinearModels......................463.2.5ParametersofLocalModeling.................463.2.6Regularization..........................483.2.7OptimizationofLocalModels.................52HandbookofTimeSeriesAnalysis.BjörnSchelter,MatthiasWinterhalder,JensTimmerCopyright©2006WILEY-VCHVerlagGmbH&Co.KGaA,WeinheimISBN:3-527-40623-9viContents3.3ClusterWeightedModeling.......................533.3.1TheEMAlgorithm........................553.4Examples..................................583.4.1NoiseReduction.........................583.4.2SignalThroughChaoticChannel................583.4.3FrictionModeling........................603.5Conclusion.................................63References....................................644DeterministicandProbabilisticForecastinginReconstructedStateSpaces(HolgerKantzandEckehardOlbrich)674.1Introduction................................674.2DeterminismandEmbedding......................694.3StochasticProcesses............................754.4EventsandClassificationError.....................814.5Conclusions................................85References....................................865DealingwithRandomnessinBiosignals(PatrickCelka,RolfVetter,EllyGysels,andTrevorJ.Hine)895.1Introduction................................895.1.1Determinism:DoesItExist?...................905.1.2Randomness:AnIllusion?....................905.1.3RandomnessandNoise.....................925.2HowDoBiologicalSystemsCopewithorUseRandomness?...935.2.1UncertaintyPrincipleinBiology.........