分形維數(shù)的數(shù)學(xué)基礎(chǔ)及對(duì)上海股票市場(chǎng)混沌、分形特性的實(shí)證分析.pdf

1、四川大學(xué)碩士學(xué)位論文分形維數(shù)的數(shù)學(xué)基礎(chǔ)及對(duì)上海股票市場(chǎng)混沌、分形特性的實(shí)證分析姓名：李方文申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：李竹渝20030324四川大學(xué)碩士學(xué)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