分形維數(shù)的數(shù)學基礎及對上海股票市場混沌、分形特性的實證分析.pdf

1、四川大學碩士學位論文分形維數(shù)的數(shù)學基礎及對上海股票市場混沌、分形特性的實證分析姓名：李方文申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：李竹渝20030324四川大學碩士學位論文Mathematicalbasisofthefractal—dimensionandempiricalanalysisofthechaosandfractaltoShanghaistockmarketMajor：AppliedMathematicsGraduateS

2、tudent：LbFangwenSupervisor：LiZhuyuAbstractThetheoryofchaosandfractalhavearewidelyappliedoneconomicsandfinancefieldsincethe70’SlastcenturyTalkingaboutourcountry’Sstudiesonthiswayaswhole，thesestudiesasfollowedhavebeendoing

3、，recognizingofsystemchaos，lookingforchaosattractors，researchingfractalstructuretotimeseriescurvepredictionandcontroltochaossystemetcAUthosestudiesneeddealwiththeestimationofthefractaldimensionTherearemanydefinitionsandes

4、timationmethodsofthefractal—dimensioninpracticalappliedThereforeitiSnecessarytodiscussthemathematicalbasisandcalculationmethodsofthefractaldimensionandrecognizingthedefinitionandmutualcorrelationofmanyusefulfraetal—dimen

5、sionThechapteroneofthispaperweintroducetheapplicationofchaosandfractaIineconomicsandfinance，giveOuttheknowledgeofthecorrelationtochaosandfractalandpointoutthattheestimationofthefractaldimensioniSveryimportantinresearchIn

6、chaptertwoandchapterthreewediscussinsomedetailthemathematicstheoryandestimatemethodsofthefractal—dimensionincludingthemathematicaldefinitionandappliedcharactersofalmostallthefractaldimensionSpeciallywegiveoutestimationma

7、nnersofcorrelationdimensionandHttrstexponentthatarewidelyusedwhilecalculatingthefractaldimensionofatimeseriesAtlastthroughestimatingthecorrelationdimansionandHurstexponenttoShanghaiStockIndexwegivesomeempiricalanalysisab

8、outthecharactersofchaosandfractalonShanghaistockmarketbyusingSASandMATLABComputationresultsonrealdatafromShanghaistockmarketobviouslyshowthatthefractaldimensiononShanghaistockmarketisapproximately15AndfurthermoreShanghai