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1、Randommatrixapproachtodynamicevolutionofcross-correlationsintheChinesestockmarketFeiRen1;2andWei-XingZhou1;2;31SchoolofBusiness,EastChinaUniversityofScienceandTechnology,Shanghai200237,China2ResearchCenterforEconophysics,EastChinaUniversityofScienceandTech
2、nology,Shanghai200237,China3SchoolofScience,EastChinaUniversityofScienceandTechnology,Shanghai200237,ChinaE-mail:wxzhou@ecust.edu.cn(Wei-XingZhou)Abstract.Westudythedynamicevolutionofcross-correlationsintheChinesestockmarketmainlybasedontherandommatrixtheo
3、ry(RMT).Thecorrelationmatricesconstructedfromthereturnseriesof367A-sharestockstradedontheShanghaiStockExchangefromJanuary4,1999toDecember30,2011arecalculatedoverarollingwindowwithasizeof400days.Asaconsequence,athoroughstudyofthevariationoftheinterconnectio
4、namongstocksanditsunderlyinginformationindierenttimeperiodsisconducted.Theevolutionsofthestatisticalpropertiesofthecorrelationcoecients,eigenvalues,andeigenvectorsofthecorrelationmatricesarecarefullyanalyzed.Wefindthatthestockcorrelationsaresignificantlyinc
5、reasedintheperiodsoftwomarketcrashesin2001and2008,andthesystemicriskishigherinthevolatileperiodsthancalmperiods.Byinvestigatingthesignificantcontributorsofthelargeeigenvectorsindierentrollingwindows,weobserveadynamicevolutionbehaviorinbusinesssectorssuchasI
6、T,electronics,andrealestate,whicharethoseindustriesleadingtherise(drop)before(after)thecrash.Submittedto:NewJ.Phys.arXiv:1308.1154v1[q-fin.ST]6Aug2013CONTENTS2Contents1Introduction22Dataandconstructionofcorrelationmatrix43Evolutionsofstatisticalpropertieso
7、fcorrelationcoecients53.1Distributionofcorrelationcoecients.....................53.2Meancorrelationcoecient..........................54Dynamicbehaviorsofeigenvaluesandtheirexplanationsofsystemvariance64.1Distributionofeigenvalues........................
8、...64.2Numberofeigenvaluessignificantlydeviatefromrandomcorrelationmatrix.74.3Portionofsystemvarianceexplainedbyeigenvalues..............85Evolutionsofstatisticalpropertiesofeigenvectorsandtheirinterpretations
