一种新的考虑时间和空间的相关系数及其算例

一种新的考虑时间和空间的相关系数及其算例宋马林1王舒鸿2汝慧萍2(1安徽财经大学统计与应用数学学院;2南开大学经济学院数量经济研究所)!本文从时间和空间多维的视角,通过分析全局MoransI相关系数与局部MoransI相关系数的特点,提出一种新的考虑时空的相关系数分析方法然后将中国内地各省份的专利授权数指标的多维分析作为算例,应用这种新的时空相关系数进行定量分析,其结果不仅与Moran相关系数的分析结果高度正相关,并具有后者所不具有的能够同时分析空间和时间指标变化趋势的优势同时考虑时间和空间因素的相关系数,为社会经济时空变化的空间计量分析提供了新的工具时空相关系数空间计量经济学Moran相关系数F2240AANewCorrelationCoefficientConsideringSpace-TimeFactorsandItsIllustrationAbstract:Fromtheperspectiveofmulti-dimensionofspaceandtime,thisarticleproposesanewcomputationalmethodofcorrelationcoefficientconsideringbothtemporalandspatialfactors,basedontheanalysisofthecharacteristicsofGlobalMoransIcorrelationcoefficientandlocalMoransIcorrelationcoefficientThenthepatentauthorizationquantitiesofChinesemainlandsprovincesandmunicipalitiesaretakenasanexampleofmulti-dimensionalanalysisTheresultsofthenewquantitativeanalysisshowthattheoutcomesofthisnewcorrelationcoefficientisnotonlyhighlycorrelatedwithMorans,butalsohaveadvantages,analyzingthetrendsofbothtemporalandspatialindicatorssimultaneouslyThisnewcorrelationcoefficientmayprovideamorescientificandeffectivetoolforspatialeconometricanalysisintimeandspacechangesofsocietyandeconomyKeywords:Space-TimeCorrelationCoefficient;SpatialEconometrics;MoranCorrelationCoefficient∀142∀#∃20107:(70901069)(AHSK07-08D25)(2009GG10010003)(2008RKA086),()(,)(,)(Cross-SectionalData)(PanelData)()()(Anselin,1988),,,(Anselin,19921999;AnselinRey,1997;PaceBarry,1998)Anselin(1988),,,,(2004),,,(2006),281978~2002GDP,,Moran1950,w,,,,Moran,,,,Moran,,,,,,:(1)%,(Henderson,1995;CinganoSchivardi,2004),Hefindal(Combes,2000;Gao,2004),,(Kim,1995;AudretschFeldman,1996)(2),,EG(Devereux,2004)(3),,(DurantonOverman,2005)∀143∀,,,;,,,,,,,ABCD,AB,CD,ABCDabcd,11ABCD1,abAB,ABS1;,cdCD,CDS2,S1S2T,,AC,BD,ACRACBDRBDMoran(1950)MoranIMoransI,,:MoransI=&ni=1&nj=1wij(xi-x)(xj-x)&ni=1&nj=1wij∋1n&ni=1(xi-x)2(1),w:w=1ij0(2),xixjij,xCliffOrd(1981)Goodchild(1986),,MoransIEN(I)VarN(I):∀144∀#∃20107EN(I)=-1n-1(3)VarN(I)=1w20(n2-1)(n2w1-nw2+3w20)-E2N(I)(4),w0=&ni&njwijw,w1=12&ni&nj(wij+wji)2,w2=&ni(wi+wi)2,Moran:Ii=(xi-x)&nj=1wij(xj-x)1n&nj=1(xi-x)2(5),Iii,Moranw,,Tobler(1970),,,Tobler(ToblersFirstLaw,TFL),w,,,w:wij=1-dijmaxdij(6)(6),dij,maxdij,:dij=(x1-x2)2+(y1-y2)2(7)!ww,Moran,,,GDP(2),,(,Space-TimeCorrelationCoefficient,S-TCorrelationCoefficient)n,m,:Rij=&mt=1(xit-!w∀x)(xjt-!w∀x)&mi=1(xit-!w∀x)2&mi=1(xjt-!w∀x)2(8),Rijij,Rij([-1,1],xitit,xi,(8),∀145∀,,,,(8),,(8)(6),,:Rij=wij∋&mt=1(xit-!w∀x)(xjt-!w∀x)&mi=1(xit-!w∀x)2&mi=1(xjt-!w∀x)2(9),,,Moran,2000~2008Moran,1天津的时空相关系数2000~2008,GeoDa95,;,,(6)11wXYXYXY11670402100501117213207003971015930400024411742394500487119132559003041072127110027511702390900494115672733003281009124640018811156373300413119953702004528810302700067116574694003951142334140041410938358900377122373997004311119430800035710260365200288127514292003511114527400031196773499002031287248590029611313221200249106143696003381214931390037410825225600230820942880000012001330600404110831735001761215529190034510790297300309:GeoDa95(6)(7)(9),1,S-T,2,2S-T2000~2008∀146∀#∃201072S-TS-TS-TS-T1000000000-0387108948-00960-0393407955-01390-0395207391-02181-0415107208-02186-0423906846-02495-0432004756-02508-0475703245-02882-0534302111-02897-0540301018-0303300080-03598:(9)2Moran空间相关评价(1)Rookw,Moran01968,(3)(4),(2)22,2008,w,;,5%,,∀147∀,2,,(++),(-+),(--),(+-)(++)(--),,;(-+),,;(+-),,;332008:(1)(2)(3)(4)Moran3D,X-Y,XY,ZMoran(3)3,,,X-Y,32008Moran,2000~20089Moran,∀148∀#∃20107(+-)(++),(-+)(--),1(++),2(+-),-1(--),-2(-+),0;1,2,03442000200120022003200420052006200720081111111119111111111911111111191000111116111110-2-2-2-1-2-2-2-2-2-2-2-2-2-18-2-2-2-2-2-2-2-2-2-18-2-2-2-2-2-2-2-2-2-18-2-2-2-2-2-2-2-2-2-18-2-2-2-2-2-2-2-2-2-18222222222182222222221822222222016-1-1-1-1-1-1-1-1-1-9-1-1-1-1-1-1-1-1-1-9-1-1-1-1-1-1-1-1-1-9-1-1-1-1-1-1-1-1-1-9-1-1-1-1-1-1-1-1-1-9-1-1-1-1-1-1-1-1-1-9-1-1-1-1-1-1-1-1-1-9-1-1-1-1-1-1-1-1-1-9-1-1-1-1-1-1-1-1-1-9-1-1-1-1-1-1-1-1-1-9-1-1-1-1-1-1-1-1-1-9-1-1-1-1-1-1-1-1-1-9-1-1-1-1-1-1-1-1-1-9-1-1-1-1-1-1-1-1-1-9-1-1-1-1-1-1-1-1-1-9∀149∀()200020012002200320042005200620072008222-10-102281-20000000-10000000000Moran00900075300968017330099701091014910190901968P-Value008130054500472039700100400005000:GeoDa954Moran,MoranP,,,,,2000~2008(4),2000~20089,;;3时空相关系数与Moran分析结果对比,,Moran(5)5,9S-T,,9;,S-T,,;9,S-T,,5S-TS-TS-TS-T100001800000-9-03871-1089486-00960-9-03934-9079559-01390-18-03952-90739116-02181-9-04151-18072089-02186-18-04239-18068469-02495-9-04320-90475618-025080-04757-9032458-02882-9-05343-902111-1-02897-9-05403-901018-9-03033-1800080-9-03598-9:24∀150∀#∃20107S-T[05,1],;[0,05],;[-05,0],;[-1,-05],S-TMoran,(4)4S-T4,1strange2ndrange3rdrange4thrange,,,,,,S-T04756,,S-T08352,,S-T,,S-T,,MoranMoran,,,,Moran,,)∗,)∗,(SAR):y=+Wy+!(10),,!,,WMoran,w,y,,∀151∀,,,SAR,,SAR,,,VAR,S-TVAR,[1]Anselin,L,1988,SpatialEconometrics:MethodsandModels[M],Dordrecht:KluwerAcademic[2]Anselin,L,1992,SpaceandAppliedEconometrics:Introduction[J],RegionalScienceandUrbanEconomics,22(3),307~316[3]Anselin,L,19