medium and smallscale analysis of financial data（中小规模的金融数据分析外文翻译学士学位论文.doc

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1、Mediumandsmall-scaleanalysisoffinancialdataAbstractAstochasticanalysisoffinancialdataispresented.Inparticularweinvestigatehowthestatisticsoflogreturnschangewithdifferenttimedelayst.Thescale-dependentbehaviouroffinancialdatacanbedividedintotworegions.Thefirst

2、timerange,thesmall-timescaleregion(intherangeofseconds)seemstobecharacterisedbyuniversalfeatures.Thesecondtimerange,themedium-timescalerangefromseveralminutesupwardscanbecharacterisedbyacascadeprocess,whichisgivenbyastochasticMarkovprocessinthescaleτ.Acorres

3、pondingFokker–Planckequationcanbeextractedfromgivendataandprovidesanon-equilibriumthermodynamicaldescriptionofthecomplexityoffinancialdata.Keywords:Econophysics;Financialmarkets;Stochasticprocesses;Fokker–Planckequation1.IntroductionOneoftheoutstandingfeatur

4、esofthecomplexityoffinancialmarketsisthatveryoftenfinancialquantitiesdisplaynon-Gaussianstatisticsoftendenotedasheavytailedorintermittentstatistics.Tocharacterizethefluctuationsofafinancialtimeseriesx(t),mostcommonlyquantitieslikereturns,logreturnsorpriceinc

5、rementsareused.Here,weconsiderthestatisticsofthelogreturny(τ)overacertaintimescalet,whichisdefinedasy(τ)=logx(t+τ)-logx(t),(1)wherex(t)denotesthepriceoftheassetattimet.Acommonproblemintheanalysisoffinancialdataisthequestionofstationarityforthediscussedstocha

6、sticquantities.Inparticularwefindinouranalysisthatthemethodsseemtoberobustagainstnonstationarityeffects.Thismaybeduetothedataselection.Notethattheuseof(conditional)returnsofscaleτcorrespondstoaspecificfilteringofthedata.Neverthelesstheparticularresultschange

7、slightlyfordifferentdatawindows,indicatingapossibleinfluenceofnonstationarityeffects.Inthispaperwefocusontheanalysisandreconstructionoftheprocessesforagivendatawindow(timeperiod).TheanalysispresentedismainlybasedonBayerdataforthetimespanof1993–2003.Thefinanc

8、ialdatasetswereprovidedbytheKarlsruherKapitalmarktDatenbank(KKMDB).2.Small-scaleanalysisOneremarkablefeatureoffinancialdataisthefactthattheprobabilitydensityfunctions(pdfs)arenotGaussian,butexhi