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1、ChapterElementsofExploratoryTimeSeriesAnalysis1Atimeseriesisasequenceofobservationsthatarearrangedaccordingtothetimeoftheiroutcome.Theannualcropyieldofsugar-beetsandtheirpricepertonforexampleisrecordedinagriculture.Thenewspa-pers'businesssectionsreportdailystockprices,weeklyinteres
2、trates,monthlyratesofunemploymentandannualturnovers.Meteorologyrecordshourlywindspeeds,dailymaximumandminimumtempera-turesandannualrainfall.Geophysicsiscontinuouslyobservingtheshakingortremblingoftheearthinordertopredictpossiblyimpend-ingearthquakes.Anelectroencephalogramtracesbrai
3、nwavesmadebyanelectroencephalographinordertodetectacerebraldisease,anelectrocardiogramtracesheartwaves.Thesocialsciencessurveyan-nualdeathandbirthrates,thenumberofaccidentsinthehomeandvariousformsofcriminalactivities.Parametersinamanufacturingprocessarepermanentlymonitoredinorderto
4、carryoutanon-lineinspectioninqualityassurance.Thereare,obviously,numerousreasonstorecordandtoanalyzethedataofatimeseries.Amongtheseisthewishtogainabetterunder-standingofthedatageneratingmechanism,thepredictionoffuturevaluesortheoptimalcontrolofasystem.Thecharacteristicpropertyofati
5、meseriesisthefactthatthedataarenotgeneratedindepen-dently,theirdispersionvariesintime,theyareoftengovernedbyatrendandtheyhavecycliccomponents.Statisticalproceduresthatsupposeindependentandidenticallydistributeddataare,therefore,excludedfromtheanalysisoftimeseries.Thisrequiresproper
6、meth-odsthataresummarizedundertimeseriesanalysis.2ElementsofExploratoryTimeSeriesAnalysis1.1TheAdditiveModelforaTimeSeriesTheadditivemodelforagiventimeseriesy1;:::;ynistheassump-tionthatthesedataarerealizationsofrandomvariablesYtthatarethemselvessumsoffourcomponentsYt=Tt+Zt+St+Rt;t
7、=1;:::;n:(1.1)whereTtisa(monotone)functionoft,calledtrend,andZtre
ectssomenonrandomlongtermcyclicin
uence.Thinkofthefamousbusinesscycleusuallyconsistingofrecession,recovery,growth,anddecline.Stdescribessomenonrandomshorttermcyclicin
uencelikeaseasonalcomponentwhereasRtisarandomvari
8、ablegraspingallthedeviatio
