股票收益率的尖峰厚尾分布

股票收益率的尖峰厚尾分布FATTAILDISTRIBUTIONOFSTOCKRETURNS指导教师：申请学位级别：学士论文提交日期：2014年6月摘要在经济活动占主导地位的现代社会里，不管是各国的金融机构、监管当局还是社会各界都对收益率寄予了极大的关注。自对收益率的研究以来人们在很长时间里都假设收益率是服从正态分布的，但是经验分布直观显示正态分布并不能很好的拟合收益率的分布特征，国内外对这一发现也进行了深刻的探索，并提出了好多的分布函数去拟合收益率的分布。虽然在之后的研究中发现有好多的分布对收益率的拟合效果都优于正态函数，究竟收益率服从何种分布至今并无定论。搞清楚股票收益率等金融时间序列数据所服从的分布对金融风险的度量是至关重要的，大量研究表明，股票收益率等金融时间序列数据具有“尖峰厚尾”的分布特征，用正态分布和t分布都无法描述这种分布特征。本研究在一元线性回归分析的基础上提出了一种尖峰厚尾分布，并对沪深股市收益率进行了实证分析，给出了参数估计的方法，该分布能很好的描述沪深股市收益率的分布特征。在参数估计的过程中，本文运用了两种方法一种是直接用最大似然估计，另一种是将一元线性回归和最大似然估计结合在一起来估计收益率的密度函数中的参数，而这两种方法的实现都借助了MATLAB数学软件。最后采用了KS检验对拟合度进行了检验，发现这种分布可以很好地拟合股票收益率的分布。关键词：股票收益率；尖峰厚尾；一元线性回归；最大似然估计；K-S检验ABSTRACTInmordensocietywhereeconomicactivityispredominant,whetherthenationalfinancialinstitutions,regulatoryauthoritiesorthecommunitiespaygreatattentiontotherateofreturn.Inaverylongtimepeoplehaveassumedthattheyieldisnormallydistributedinitsstudyoftherateofreturn,buttheempiricaldistributionvisualizethatnormaldistributionisnotagoodfityieldtomatchdistributedcharacteristicofrateofreturn,domesticandoverseasalsomadeaprofoundexplorationtothefindingsandusedalotofthedistributionfunctiontofitthedistributionofyields.Althoughthestudyfoundthattherearealotdistributionstoyield’simitativeeffectthataresuperiortonormalfunction,whatdistributiontheyieldobedienttohasbeennoconclusive.Makingclearthatwhatdistributionstockreturnsandotherfinancialtimeseriesdataobeyiscriticaltothefinancialrisk,alargenumberofstudieshaveshownthatstockreturnsandotherfinancialtimeseriesdataisadistributionoffattail,andthenormaldistributionandtdistributioncannotdescribeitsdistributionfeature.Onthebasisofalinearregressionanalysisthearticleproposesafattail,peakedandskeweddistribution,andmakesanempiricalanalysistotheShanghaiandShenzhenstockyields,givingtheparameterestimationmethod,thedistributioncanwelldescribetheShanghaiandShenzhenstockmarket’sreturnsdistributionrates.Intheprocessofparameterestimation,thispaperusestwotypesofmethodtoestimateparameter,oneisthedirectlyusingmaximumlikelihoodestimation,theotherisalinearregressionandmaximumlikelihoodestimationcombinedtoestimatethedensityfunctionofyieldstheparameters,therealizationofthesetwomethodsiswiththehelpoftheMATLABmathematicalsoftware.Finally,theKStestforgoodnessoffitwastestedandfindingthatthisdistributioncanbeagoodfitforthedistributionofstockreturns.KeyWords:Stockreturns;fattail;linearregression;maximumlikelihoodestimation;KStest目录1绪论..........................................................................................................................11.1引言..................................................................................................................11.2研究背景与意义..............................................................................................11.3国内外研究现状..............................................................................................31.4论文的研究思路与组织结构..........................................................................41.5本章小结..........................................................................................................52股票收益率尖峰厚尾性检验...........................................................................62.1股票收益率计算方法......................................................................................62.2收益率正态检验和尖峰厚尾性......................................................................72.3尖峰检验法......................................................................................................82.4厚尾检验法.....................................................................................................112.5本章小结........................................................................................................133股票收益率分布模型.......................................................................................143.1几种常用收益率分布模型............................................................................143.2基于正态比值法收益率分布模型................................................................183.3拟合优度检验.................................................................................................223.4本章小结........................................................................................................234中国股票市场收益率分布实证分析...........................................................244.1数据选取及正态检验....................................................................................244.2中国股票收益率尖峰厚尾性检验................................................................264.3股票收益率的尖峰厚尾分布........................................................................284.4本章小结........................................................................................................355结论与展望..........................................................................................................365.1结论................................................................................................................365.2展望................................................................................................................36参阅文献..................................