elements of exploratory time series analysis

elements of exploratory time series analysis

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时间:2018-02-10

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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

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