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

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1、Mediumandsmall-scaleanalysisoffinancialdataAbstractAstochasticanalysisoffinancialdataispresented.Inparticularweinvestigatehowthestatisticsoflogreturnschangewithdifferenttimedelayst.Thescale-dependentbehaviouroffinancialdatacanbedividedintotworegions.Thefirsttimerange,thesma

2、ll-timescaleregion(intherangeofseconds)seemstobecharacterisedbyuniversalfeatures.Thesecondtimerange,themedium-timescalerangefromseveralminutesupwardscanbecharacterisedbyacascadeprocess,whichisgivenbyastochasticMarkovprocessinthescaleτ.AcorrespondingFokker–Planckequationcanb

3、eextractedfromgivendataandprovidesanon-equilibriumthermodynamicaldescriptionofthecomplexityoffinancialdata.Keywords:Econophysics;Financialmarkets;Stochasticprocesses;Fokker–Planckequation1.IntroductionOneoftheoutstandingfeaturesofthecomplexityoffinancialmarketsisthatveryoft

4、enfinancialquantitiesdisplaynon-Gaussianstatisticsoftendenotedasheavytailedorintermittentstatistics.Tocharacterizethefluctuationsofafinancialtimeseriesx(t),mostcommonlyquantitieslikereturns,logreturnsorpriceincrementsareused.Here,weconsiderthestatisticsofthelogreturny(τ)ove

5、racertaintimescalet,whichisdefinedasy(τ)=logx(t+τ)-logx(t),(1)wherex(t)denotesthepriceoftheassetattimet.Acommonproblemintheanalysisoffinancialdataisthequestionofstationarityforthediscussedstochasticquantities.Inparticularwefindinouranalysisthatthemethodsseemtoberobustagains

6、tnonstationarityeffects.Thismaybeduetothedataselection.Notethattheuseof(conditional)returnsofscaleτcorrespondstoaspecificfilteringofthedata.Neverthelesstheparticularresultschangeslightlyfordifferentdatawindows,indicatingapossibleinfluenceofnonstationarityeffects.Inthispaper

7、wefocusontheanalysisandreconstructionoftheprocessesforagivendatawindow(timeperiod).TheanalysispresentedismainlybasedonBayerdataforthetimespanof1993–2003.ThefinancialdatasetswereprovidedbytheKarlsruherKapitalmarktDatenbank(KKMDB).2.Small-scaleanalysisOneremarkablefeatureoffi

8、nancialdataisthefactthattheprobabilitydensityfunctions(pdfs)arenotGaussian,butexhi