ֻ28जֻ7௹॥ᇅંაႋႨ୍7ᄅControlTheory&໓ᅣщݼ:1000−8152(2011)07−0979−08ཟਈሱ݂߭ଆGrangerၹݔ่֥ࡱྐ༏я്აႋႨ້ᄃᗘ1,2,โ᫋1,ӧᅝ൰1(1.༆К۽ြն࿐ႋႨඔ࿐༢,༆༆ν710129;2.߉Кഽٓն࿐ඔ࿐॓࿐࿐ჽ,νߪ߉К235000)ᅋေ:Grangerၹݔྟ൞ޙਈ༢эਈࡗܱ༢֥ᇗေ၇ऌ.Ԯ֥ਆэਈGrangerၹݔٳ༅مಸၞӁളເၹݔܱ༢,҂ିख़߂эਈࡗ֥ࠧൈၹݔྟ.Ч໓০Ⴈଆٚم࣮ൈࡗਙэਈࡗ֥Grangerၹݔܱ༢,ࡹ৫ਔൈࡗਙGrangerၹݔ,ิԛਔGrangerၹݔ่֥ࡱྐ༏я്ٚم,০Ⴈࠁᚧંᇏ֥ܱ৳ࠒٳܙ࠹่ࡱྐ༏,࠹ਈ֥ཁᇷྟႮᇂߐဒಒק.ٟᆇࢲݔᆣൌਔٚم֥Ⴕིྟ,ѩ০Ⴈھٚم࣮ਔॢగಙᆷѓၛࠣᇏݓܢ൧ࡗ֥Grangerၹݔܱ༢.ܱՍ:Grangerၹݔ;؟ົൈࡗਙ;่ࡱྐ༏;ܱ৳ࠒٳ;ᇂߐဒᇏٳোݼ:໓ངѓ്:AIdentificationandapplicationaboutGrangercausalitygraphofvectorautoregressivemodelusingconditionalmutualinformationWEIYue-song1,2,TIANZheng1,CHENZhan-shou1(,NorthwestPolytechnicalUniversity,Xi’anShaanxi710129,China;,HuaibeiNormalUniversity,HuaibeiAnhui235000,China)Abstract:’:Grangercausalitygraph;multivariatetimeseries;conditionalmutualinformation;correlationintegral;permutationtests1ႄ(Introduction)ཋᇅਔھဒٚم֥Ⴈٓຶ.Ⴎܴҩඔऌಒק༢эਈࡗ֥ၹݔܱ༢൞༢୍࣍ট,০Ⴈଆٚم࣮༢эਈࡗ֥۲я്֥ᇗေଽಸ.ሱՖ1969୍Granger[1]ิԛGrangerᇕཌྷ၇ܱ༢ࠆ֤ਔᇭ؟࿐ᆀ֥ܱᇿ.ଆٚم҂ၹݔྟۀၛট,GrangerၹݔྟၘࣜӮູޙਈ༢ࣇିܔࢹᇹႿᆰܴ֥іൕ෮ေ࣮ଢѓᆭࡗ֥эਈࡗܱ༢֥ᇗေ၇ऌ,ᄝപࣜຩ[2]aࣁವཌྷ၇ܱ༢,طॖ০Ⴈ֥ࢲܒؓھཌྷ၇ܱ༢ࣉྛࣜ࠶[3]a၄࿐[4]aྐݼԩ[5]֩ᇙ؟ਵთႵሢܼٗٳ༅,ၘࣜӮູٳ༅ބԩ༢эਈࡗگᄖܱ༢ႋႨ.Grangerᆷԛ:ೂݔᄝఃჅэਈྐ༏۳ק֥౦֥၂۱ᇗေ۽ऎ[8∼10].০Ⴈଆٚم࣮эਈࡗঃ༯,ವೆଖ၂эਈ֥ྐ༏ႵᇹႿؓਸ਼၂эਈࡼট֥Grangerၹݔྟ൮༵ႮDahlhausބEichler[11]ิԛ,ᆴ֥ყҩ,ᄵھэਈ൞ਸ਼၂۱эਈ֥ჰၹ.֒భؓEichler[12,13]ؓఃቔਔࣉ၂֥࣮҄,ᄝࡌഡэਈڛ༢эਈࡗGrangerၹݔܱ༢֥࣮؟ҐႨਆэਈՖᆞٳ֥༵҃ဒྐ༏༯,০Ⴈ่ࡱᆞࢌྟࡹ৫Grangerၹݔྟဒم[6,7],ႮႿޭ൪ఃᇗေࢳਔGrangerၹݔଆ.่ࡱᆞࢌྟᆺൡކႿٳ༅эਈ֥႕ཙ,ӈ߶֝ᇁເၹݔྟ֥ԛགྷ.Վຓ,ਆэᆞэਈࡗ֥ၹݔܱ༢,ؓႿэਈٳ҃ໃᆩࠇڛՖਈGrangerၹݔྟဒᆺିဒਆэਈࡗӉ௹֥ၹ٤ᆞٳ҃ൈ,০Ⴈଆٚم࣮эਈࡗ֥ၹݔݔܱ༢,طم؇ਈэਈࡗ֥ࠧൈၹݔܱ༢,ᆃུྟၛࠣႵི֥я്Grangerၹݔࢲܒ൞ಯր࣮൬۠ರ௹:2010−06−30;൬ྩڿ۠ರ௹:2011−02−23.ࠎࣁཛଢ:ݓࡅሱಖ॓࿐ࠎࣁሧᇹཛଢ(60375003,10926197).
980॥ᇅંაႋႨֻ28ज֥໙ี.2)ؓၩi,j∈Vi6=jႵЧ໓࣮ٳ҃ໃᆩ֥ൈࡗਙGrangerၹݔྟ֥(i,j)∈/Eu⇔Xj(t)⊥Xi(t)|X¯V(t),XV\{i,j}(t).ଆя്໙ี.๙ݖ่ࡱ৫ྟࡹ৫؟ົൈࡗਙႮഈඍקၬॖၛुԛ,ೂݔXA൞XBܱႿXV֥Grangerၹݔ,ൈᄝGrangerၹݔᇏವೆࠧൈၹݔྟܱ༢,ิԛਔGrangerၹݔ่֥ࡱྐ༏я٤Grangerჰၹ,ᄵᄝ۳קX¯V\A(t)֥౦ঃ༯,XB(t)ބX¯A(t)൞่ࡱ৫֥,ᆃ෮၇ঠ֥ྐ༏്ູࠢٚم,০Ⴈܱ৳ࠒٳܙ࠹่ࡱྐ༏.ູਔх૧ٳX༅࠹ਈ࣍රٳ҃෮ླ֥၂ུگᄖ࠹ෘ,ҐႨᇂߐV(t),ࡼXV(t)ႨX{A,B}(t)টูս,֤֥֞ᄵ൞ਆэਈGrangerၹݔܱ༢.ဒمಒק࠹ਈ֥ཁᇷྟ,ѩ০Ⴈ෮۳ٚمቓਔקၬ3(ਆэਈGrangerၹݔܱ༢)ؓႿnົଆٳ༅ބൌ২ٳ༅.აԮ֥ਆэਈGrangerၹݔ໗ෛࠏݖӱX(t)=(X1(t),X2(t),···,Xn(t))T,ྟٳ༅ٚمཌྷб,෮۳֥ଆٚمି۷ࡆᆰܴ֥Xj(t)⊥X¯i(t)|X¯{i,j}\X¯i(t)Ӯ৫,ᄵӫXi(t)൞Xj(t)ࢣൕٳਈࡗ֥؟ᇕၹݔܱ༢,္ॖဒ؟۱эਈࡗ֥ܱႿX{i,j}֥ਆэਈ٤Grangerჰၹ.֥Grangerၹݔܱ༢,ൈି֤֞۷ູሙಒ֥ࢲં.ਬनᆴ໗VAR(p)ଆॖіൕູ2؟ົൈࡗਙGrangerၹݔ(GrangerpX(t)=∑AkX(t−k)+ut,(1)causalitygraphformultivariatetimeseries)k=1V൞၂٤ॢႵཋࠢ,G=(V,E)൞၂Ⴕࠢ,ఃᇏ:X(t)=(X1(t),X2(t),···,Xn(t))T,ut=(u1t,ఃᇏVᇏ֥ჭӫູ֥פׄ,طE={(a,b)|a,b∈···,unt)Tູ৫ٳ֥҃ྍ༏ཛ,E(ut)=V}ᇏ֥ჭӫູш0,Σ=E(utuTt)ູ٤అၳᆔ;A1,···,Ap൞n×nࢨ.(a,b)∈E(b,a)∈E,ᄵ(a,b)ӫູGᇏ֥ཟш༢ඔइᆔ.ູਔ۳ԛཟਈሱ݂߭ଆ(vectorautore-,ᄝᇏႨa—bіൕ.ೂݔgressivemodel,VAR)ଆ֥Grangerၹݔ,ᆃ༵(a,b)∈E(b,a)∈/E,ᄵ(a,b)ӫູGᇏ֥Ⴕཟш,ᄝᇏႨa→bіൕ.Gᇏ࠻ႵႵཟшႻႄႨ၂ུקၬބק.Ⴕཟш,ᄵӫఃູࠁކקၬ4(ൈࡗਙ৽[8])ؓnົ໗ൈࡗ.ഡXਙX(t)=(X(t)=(X1(t),X2(t)1t,···,Xnt)T,࠺ႮX(t),X(t−1),,···,Xn(t))T൞קၬᄝۀੱॢࡗ(Ω,F,P)ഈ֥nົ໗ෛࠏݖӱ···,X(t−p)֥۲۱ٳਈ෮ܒӮ֥ࠢކູV,,V={1,G=(V,ETS)ડቀၛ༯่ࡱ,ᄵӫఃູൈࡗ2,···,n}ູཌྷႋ֥ᆷѓࠢ.ؓၩA⊂V,ၛXA=ਙ৽ଆ.{Xa,a∈A}іൕXV=X(t)֥؟эਈሰݖӱ,X¯(t)={X(s),s<t}іൕᄝൈख़tᆭభھෛࠏݖӱ֥ྐ(a,t−u)→(b,t)∈/ETS⇔༏ࠢu60ࠇ=(V,Ed,Eu)іൕפູׄࠢV֥ࠁކ,a(t−u)⊥Xb(t)|X¯V(t)\{Xa(t−u)},ఃᇏEd⊆{(u,v)∈V×V|u(a,t−u)→(b,t)∈/E6=v}ູႵཟшࠢ,TS⇔طEu⊆{(u,v)∈V×V|u6=v}ູཟшࠢ.u60ࠇXa(t)⊥Xb(t)|X¯V(t)∪{XV\{a,b}(t)}.קၬ1(Grangerၹݔྟ)ഡAބB൞V֥҂ཌྷࢌႄ1[8]ؓႿVARଆ(1),G=(V,ETS)൞ཌྷሰࠢ,XAބXB൞XV֥ཌྷႋሰݖӱ,XV(t)іൕᄝႋ֥ൈࡗਙ৽ଆ,ᄵൈख़t֥෮ႵႵܱV֥ྐ༏ࠢ,(j,t−k)→(i,t)∈/ETS⇔k∈{1,···,p},1)ೂݔXB(t)⊥X¯A(t)|X¯V\A(t),ᄵӫXA൞XBܱႿXV֥٤Grangerჰၹ(ژݼ⊥іൕ৫ܱ༢);2)ೂݔXAk(i,j)=0,(j,t)−(i,t)∈/Eu⇔Σ(−1)(i,j)=0,B(t)⊥XA(t)|X¯V(t),XV\{A,B}(t),ᄵӫXAބXBܱႿXV൞٤ࠧൈၹݔ֥ఃᇏ(i,j)ູAkֻ֥(i,j)໊ᇂ֥ჭ.קၬ2ק1ؓऎႵGrangerၹݔG=(V,Ed,(Grangerၹݔ)ഡX(t)=TEu)֥VARଆ(1),ၛ༯ࢲંӮ৫:(X1(t),X2(t),···,Xn(t))1)ؓၩi,j∈{1,···,n}Ⴕ൞קၬᄝۀੱॢࡗ(Ω,F,P)ഈ֥nົ໗ෛࠏݖӱ,ೂݔၛ༯่ࡱӮ৫,ᄵӫၛ{X(t)}۲ٳਈູפׄ(i,j)∈/Ed⇔∀k∈{1,···,p},Ak(j,i)=0;(2)ࠢV={1,2,···,n}֥ࠁކG=(V,Ed,Eu)ູ2)ؓၩi,j∈{1,···,n}ႵGrangerၹݔ.(i,j)∈/Eu⇔Σ−1(i,j)=0.(3)1)ؓၩi,j∈Vi6=jႵᆣ1)ႮGrangerၹݔྟ֥קၬၛ่ࠣࡱ৫(i,j)∈/Ed⇔Xj(t)⊥X¯i(t)|X¯V\i(t);ྟ֥ྟᇉႵ
ֻ7௹້ᄃᗘ֩:ཟਈሱ݂߭ଆGrangerၹݔ่֥ࡱྐ༏я്აႋႨ981(i,j)∈/Ed⇔Xj(t)⊥X¯i(t)|X¯V\i(t)⇔Ⴎ1ॖᆩ,ཌྷؓႿᆜ۱ྐ༏ࠢXV(t),ٳਈ∀k∈{1,···,p},X1(t)ބX2(t),X1(t)ބX3(t)ᆭࡗթᄝGrangerၹXݔܱ༢,ٳਈX3(t)ބX5(t)ᆭࡗթᄝࠧൈၹݔܱ༢,j(t)⊥Xi(t−k)|X¯V(t)\Xi(t−k),طٳਈX1(t)ބX4(t)ᆭࡗ҂թᄝGrangerၹݔܱ༢,X1(t)๙ݖX3(t)ؓX4(t)Ⴕሢࡗࢤ႕ཙ,ࠧX1(t)Xj(t)⊥{X¯i(t)\Xi(t−k)}|{X¯V\i(t),Xi(t−k)}.൞X4(t)֥ࡗࢤჰၹ.ႮՎॖၛुԛ,ᆃ෮קၬ֥Ⴎႄ1ᆩGrangerၹݔିّ႘ԛэਈᆭࡗ؟ᇕၹݔܱ༢.XႮഈ૫קၬ֥Grangerၹݔཁಖ၇ঠႿྐ༏j(t)⊥Xi(t−k)|X¯V(t)\Xi(t−k)⇔ࠢXV(t),ೂݔᄝXV(t)ᇏޭ၂ུᇗေэਈ֥ྐ༏,Ak(j,i)=0.(4)ᄵॖି߶֝ᇁເၹݔܱ༢֥ԛགྷ.২ೂؓႿೂ༯طؓႿൔ֥VARଆ:Xj(t)⊥{X¯i(t)\Xi(t−k)}|{X¯V\i(t),Xi(t−k)},৵࿃ᇗگ০ႨഈඍٚمႵX1(t)=aX2(t−1)+ε1(t),X2(t)=bX3(t−1)+ε2(t),(6)Xj(t)⊥{X¯i(t)\Xi(t−k)}|{X¯V\i(t),Xi(t−k)}⇔X3(t)=ε3(t),∀u∈{1,···,p},u6=k,Au(j,i)=0.(5)ఃᇏεi(t)(i=1,2,3)൞৫ٳ֥҃ෛࠏۄಠཛ.Ⴎൔ(4)ބൔ(5)ॖᆩࢲં(1)Ӯ৫Ⴎק1ॖᆩ,ཌྷؓᆜ۱ྐ༏ࠢX.{1,2,3}(t),X3(t)൞ࢲંX(2)Ⴎႄ1ᆰࢤॖ֤.ᆣи.2(t)֥Grangerჰၹ,X2(t)൞X1(t)֥Grangerჰၹ,ᇿطX1Ⴎഈඍקॖᆩ,ൈࡗਙٳਈᆭࡗ֥3(t)൞X1(t)֥٤Grangerჰၹ.ࡼഈٚӱэྙ,GrangerၹݔྟॖႮGrangerၹݔটіൕᆺॉ੮ਆэ,ᇏਆࢲׄࡗ{ਈࡗ֥ሱ݂߭ྙൔႵթᄝႵཟшൈ,ؓႋ֥ٳਈࡗթᄝGrangerၹݔྟX1(t)=abX3(t−2)+ε˜1(t),.ਆࢲׄ(7)ࡗթᄝཟшൈ,ؓႋ֥ٳਈࡗթᄝࠧൈၹݔྟ,طࢲׄࡗX3(t)=ε3(t),ш֥թᄝაڎႻॖႮཌྷႋ֥݂߭༢ඔটಒק.ఃᇏε˜1(t)=ε1(t)+aε2(t−1).ᄵཌྷؓႿྐ༏ࠢቔູ၂۱২ሰ,1іൕਔೂ༯֥VAR(1)ଆ֥X{1,3}(t),ൔ(7)ၩሢX3(t)൞X1(t)֥Grangerჰၹ,Grangerၹݔ:ၹՎԛགྷਔເၹݔܱ༢.ႮՎॖၛुԛ,ؓႿ؟эXਈଆ,ೂݔֆॉ੮ਆэਈࡗ֥Grangerၹݔܱ(t)=AX(t−1)+ε(t),༢,طᄝཌྷܱ֥ྐ༏ࠢᇏޭ൪༢ᇏఃᇗေࢳఃᇏ:эਈ֥ྐ༏,ॖି߶֝ᇁເၹݔܱ༢֥ԛགྷ.ᆃa11a120000aൔ(7)൙ൌഈّႋ֥൞X1(t)ބX3(t)ᆭࡗ֥ਆэਈ22a2300Grangerၹݔܱ༢.A=a31a32a3300,3Grangerၹݔ֥ྐ༏ંя്ٚم00a43a44a45(IdentificationGrangercausalitygraphusing0000a55information-theoreticmethod)σ110000ؓႿၛഈ෮קၬ֥Grangerၹݔ,ေ؎ٳ0σ22σ2300Σ−1=ਈAބBᆭࡗ൞ڎթᄝཌྷႋ֥ႵཟшA→B,ᆺླ0σ32σ330σ35.؎XB(t)ބX¯A(t)ܱႿX¯V\A(t)൞ڎ่ࡱ৫.ᆃ000σ440০Ⴈྐ༏ંᇏ่֥ࡱྐ༏ট؇ਈэਈࡗ่֥ࡱ00σ530σ55৫ྟ.ഡ(X,Y,Z)൞৵࿃ෛࠏཟਈ,ෛࠏэਈX֥᧦H(X)ၛࠣXބY֥৳ކ᧦H(X,Y)ٳљູwH(X)=−[lnfX(x)]fX(x)dx,(8)wwH(X,Y)=−[lnfX,Y(x,y)]fX,Y(x,y)dxdy,(9)ఃᇏ:fX,Y(x,y)ູ৳ކۀੱૡ؇,fX(x)ູཌྷႋ֥ш1VAR(1)֥Grangerၹݔ࠽ۀੱૡ؇ݦඔ.(1)ᄝၘᆩෛࠏэਈZ่֥ࡱ༯,ෛࠏэਈXބYᆭ
982॥ᇅંაႋႨֻ28जࡗ่֥ࡱྐ༏ູStep2ෛࠏᇂߐൈࡗਙ{X}Tt=1֤ᇂߐਙI{X˜}T(X,Y|Z)=t=1;wwwfStep3࠹ෘᇂߐਙ{X˜}Tt=1֥ဒ࠹ਈ[lnX,Y|Z(x,y|z)]·fX|Z(x|z)fY|Z(y|z)I˜(·);fXStep4ᇗگStep2∼Step3BՑ;,Y,Z(x,y,z)dxdydz,(10)ఃᇏStep5࠹ෘֆшbootstrappᆴ:fX,Y|Z(x,y|z),fX|Z(x|z)ބfY|Z(y|z)ٳљູཌྷႋ่֥ࡱૡ؇.Ⴎקၬၞᆩၛ༯ࢲંӮ৫.pˆ=1+](I˜(·)>Iˆ(·))ק1+B;2ؓႿෛࠏཟਈ(X,Y,Z)ႵStep6ؓႿ࿊ק֥ཁᇷྟඣα,ೂݔpˆ6α,I(X,Y|Z)=−H(X,Y,Z)+H(X,Z)+ᄵऋध่ࡱ৫֥ჰࡌഡ.H(Y,Z)−H(Z),(11)4ଆބൌ২ٳ༅(SimulationsandcaseX⊥Y|Z⇔I(X,Y|Z)=0.(12)analysis)קЧࢫٳљ๙ݖଆٳ༅ބൌ২ٳ༅টဒ෮۳3G=(V,Ed,Eu)൞VARଆ(1)֥Grangerၹݔٚم֥Ⴕིྟ.,ᄵ২1ଆٳ༅.(i,j)∈/Ed⇔I(Xj(t),X¯i(t)|X¯V\i(t))=0,(13)ູਔဒ෮۳ٚم֥Ⴕིྟ,ᆃॉ੮ؓೂ༯ଆ(i,j)∈/Eu⇔ቔଆٳ༅,ٳљဒਙᇏэਈࡗ֥GrangerၹI(Xݔj(t),Xi(t)|X¯V(t),X¯V\{i,j}(t))=0.(14)ܱ༢ބࠧൈၹݔܱ༢:ؓႿ่ࡱྐ༏֥ܙ࠹,ࣜӈ๙ݖ༵ܙ࠹ཌྷႋ֥X1(t)=(t−1)+(t−1)+ε1(t),ۀੱૡ؇,ࣉط০Ⴈקၬ֥ٚمট֤֞.ᆃҐႨ٤Xҕඔ֥ٚمܙ࠹่ࡱྐ༏.ᄝࠁᚧ༢ٳ༅ᇏ2(t)=(t−1)+(t−1)+ε2(t),,ܱX3(t)=(t−1)+(t−1)+ε3(t),৳ࠒٳC(X,ε)൞іᆘಒקྟݖӱหᆘ֥ᇗေఃᇏ൭؍,ૌ֥ܙ࠹ཌྷؓᆰࢤ.ؓࢠཬ֥εᆴ,ܱ৳ࠒٳε(t)=(ε1(t),ε2(t),εT3(t))∼N(0,Σ),ބ᧦ᆭࡗթᄝܱ༢H(X)≈−ln[C[14](X,ε)],ၹՎॖ০Ⴈܱ৳ࠒٳ۳ԛ่ࡱྐ༏֥ܙ࠹.ܱ৳ࠒٳႮ༯ൔ۳ק:wwΣ−1=.C(X,ε)=I‖x−x′‖6εfX(x)fX(x′)dxdx′,001(15)ؓھଆ,ॉ੮n=200ބn=500ਆ۱ဢЧਈ.ఃᇏ:NູဢЧਈ,εູ࿊ᄴ֥ջॺ,I(·)ູൕྟݦඔ.3۱ٳਈਙ֥ళೆົඔ౼ູ2,ᇂߐဢЧ۱ඔ࿊ႮႿܱ৳ࠒٳ൞ނݦඔ֥௹ຬᆴ,ࠧE(I‖X−X′‖6ε),౼B=199,ᄝဒඣ༯,๙ݖଆؿགྷջၹՎॖႮU−࠹ਈ֤֥֞ܙ࠹ູॺε࿊౼бࢠކൡ.ૄᇕ౦ঃᇗگࣉྛ1000Ց,ᄵCˆཌྷႋ֥Grangerၹݔྟބࠧൈၹݔྟऋधੱࢲݔ(X,ε)=1∑N∑Nі1෮ൕ.NI(‖xi−xj‖6ε).(N−1)i=1j=1,j>iі1่ࡱ৫ྟဒ֥ऋधੱՖطཌྷႋ่֥ࡱྐ༏ܙ࠹ູTable1RejectionratesinconditionalindependencetestIˆ(X,Y|Z)=Cˆ(X,Z,ε)Cˆ(Y,Z,ε)ln.(16)Cˆ(X,Y,Z,ε)Cˆ(Z,ε)n=200n=500ູਔх૧֤֞࠹ਈ࣍රٳ҃෮ླ֥၂ུگᄖX1(t)→X2(t)࠹ෘ,ᆃ০Ⴈᇂߐဒمটקჰࡌഡ൞ڎӮ৫,X2(t)→X1(t)࿊౼ᇂߐဒم္ჷႿ֥ဒݖӱࡥֆၞྛ,X1(t)→X3(t)ܱ৳ࠒٳ֥ܙ࠹ਈCˆ൞Ց࠹ਈ֥ݦඔ,ؓᇂߐX3(t)→X1(t)ު֥ൈࡗਙЌӻཌྷ֥ࠞཋٳ҃[15]X2(t)→X3(t).ھဒݖӱॖႮၛ༯҄ᇧྙӮX3(t)→X2(t):X1(t)—X2(t)࠹ෘൈࡗਙ{X}Tt=1֥ဒ࠹ਈX1(t)—X3(t)ˆ(·);X2(t)—X3(t)
ֻ7௹້ᄃᗘ֩:ཟਈሱ݂߭ଆGrangerၹݔ่֥ࡱྐ༏я്აႋႨ983Ֆі1ᇏࢲݔॖၛुԛ,Ч໓෮۳ٚمିࢠݺ֥ҩԛൈࡗਙэਈࡗ֥Grangerၹݔܱ༢ބࠧൈၹݔܱ༢,Ⴎဒࢲݔ߂ԛ֥Grangerၹݔ2(a)ބჰଆ൞ཌྷ໖ކ֥,ࠧX1ބX2ᆭࡗ൞ູGrangerჰၹ,թᄝࠧൈၹݔܱ༢,طX2൞X3֥Grangerჰၹ.Վຓ,ෛሢဢЧਈ֥ᄹࡆ,ဒ֥൝္ෛᆭᄹն,(b)ਆэਈGrangerٳ༅م෮֤Grangerၹݔඪૼਔྐ༏ࠢᇏЇݣ֥ྐ༏ᄀ؟,ဒ֥ࢲݔ္ᄀݺ.ᇏՖX1֞X3ᆭࡗթᄝ၂่Ⴕཟਫ਼ࣥX1→X2ଆ֥Grangerၹݔ2→,X1๙ݖX2ؓX3Ӂളࡗࢤ႕ཙ.ႮႿՖX1֞X3֥෮ႵႵཟਫ਼ࣥݖX2,ၹՎᄝყҩX3ൈ,֒ྐ২2ॢగಙඔऌၹݔྟٳ༅.༏ࠢᇏݣႵX2ྐ༏ൈ,ᄹࡆX1֥ྐ༏҂߶ؓყҩࢲDahlhaus[8]০Ⴈொཌྷܱٚمٳ༅ਔݚ֣ЍݔӁളحຓ֥႕ཙ,ࠧX1൞X3֥٤Grangerჰၹ.(Heidelberg)ॢగಙඔऌࠢᇏэਈࡗ֥ཌྷ၇ࢲܒ,ູਔაЧ໓෮۳ٚمቔбࢠ,ؓھଆ္ҐႨЧ໓ࣉ၂҄ٳ༅ᆃུಙᆷѓэਈᆭࡗ֥ၹݔܱਆэਈGrangerၹݔٳ༅مٳ༅эਈࡗ֥Grangerၹ༢.ॉ੮၂သ߄ฏ(CO)a၂သ߄(NO)aؽသ߄ݔܱ༢.ॉ੮ဢЧਈn=500ൈ֥ဒ໙ี,ൌဒࢲ(NO2)aԙသ(O3)ၛࠣሹڕഝ఼؇(GRI)5۱ಙᆷݔі2,ఃᇏ:Kູᇌުࢨඔ,ژݼo9pіൕ٤ѓՖ1991୍1ᄅ֞1992୍12ᄅ֥ರ(ૄ4ཬൈ1Ց)ܴGrangerჰၹҩඔऌ,܋4386۱ܴҩᆴ..Ⴎіᇏࢲݔ෮֤֥Grangerၹݔ2(b).ෙಖਆэਈGrangerၹݔٳ༅مିᆞಒ֥я۴ऌഈࢫิԛ֥ٚم,ᇌުᆴ࿊౼k=7(۴ऌ്XAICჰᄵ࿊౼,ھᆴ္ఞݺބૄರ࿖ߌܴҩՑඔཌྷ1ބX2,X2ބX3ᆭࡗ֥ၹݔܱ༢,ؓႿ෮Ⴕ֥ᇌުᆴK,X1൞X໖ކ),ջॺ࿊౼εn=,ᇂߐဢЧ۱ඔB=199,3֥٤Grangerჰၹ֥pᆴູਬ,ၹՎؓႿཁᇷྟඣα=ཁᇷྟඣα=,ᇗگࣉྛ1000Ց,֤֥֞ࢲݔ,ऋधھࡌഡ,ࠧX1൞X3֥Grangerჰၹ,ᆃཁಖა൙ൌཌྷິМ,ၹՎႮՎі3,ཌྷႋ֥Grangerၹݔ3(a).ٚم֤֥֞X1ބXՖі3ᇏࢲݔॖၛुԛ,COބNO,COބNO2,O33ᆭࡗܱ༢൞ເၹݔܱ༢,ᆃඪૼؓ؟эਈ༢,ೂݔᄝӮؓٳ༅эਈࡗ֥ބGRI,NO2ބO3ᆭࡗऎႵචཟၹݔྟ.NOބOGrangerၹ3ݔྟൈޭఃᇗေэਈ֥ྐ༏,ಸၞ֝ᇁເၹݔᆭࡗીႵᆰࢤ֥ၹݔܱ༢,NOԢ൳CO֥႕ཙᆭຓ,ܱ༢္ބGRIႵܱ,ؓGRI֥႕ཙࢠཬ.၂۱бࢠห.љ֥ࢲં൞NOބNO2ᆭࡗીႵᆰࢤ֥ၹݔܱ༢,і2ਆэਈGrangerၹݔٳ༅مpᆴૌᆭࡗ൞๙ݖCOࡗࢤࡆၛ႕ཙ,ၹՎॖၛ๙Table2Thep–valueoftwo-variableGrangerݖᇭೂ॥ᇅCO֥ஆ٢֩ٚمࢆ֮ॢగᇏ֥သcausalityanalysismethod߄NOx֥ݣਈ,Ֆطղ֞࣪߄ॢగི֥ݔ.Վຓ,ՖGrangerၹݔ3(a)္ᆣൌਔ၂ུܻ߄࿐ં:ՖKGRI֞NO2֥ႵཟшᆣൌਔNO2֥ܻٳࢳં,12345NO2֥ളӮ֒ಖ္҂षടࠣCO֥ሱႮࠎّႋ,XطO3֥ᄹࡆ္၇ঠႿNO2֥ᄹࡆބGRI֥ࢆ֮,֥ᄹࡆᄵ߶֝ᇁGRI֥ࡨ,طO3,NOބNO2֩Xэ߄֥ᇶေჰၹ൞ܻڕഝ఼؇෮थק֥ܻ߄࿐ّႋ[16].ཌྷбࢠط,ਆэਈGrangerၹݔٳ༅م(ࢲݔі4,ཌྷႋ֥ၹݔ3(b))ෙಖ္ି؎ԛCOބNO,COބNO2,NO2ބO3ᆭࡗ֥චཟၹݔྟ,֤֥֞O3ؓGRIᆰࢤ႕ཙ֥ࢲંཁಖބၘႵંᆩ്ཌྷᙣ.Վຓ,ႵܱNO൞O3֥GrangerჰၹၛࠣNOބNO2֥චཟၹݔྟ֥ં؎ଢభ္ಌكંᆦӪ.ᇿ2і3ᇏభ5ྛඔऌіൕGrangerၹݔྟඔऌ,ၹݔٚཟՖіᇏਙэਈᆷཟྛэਈ.іᇏުྛіൕࠧൈၹݔྟඔऌ.(a)ଆ෮֤ଆ֥Grangerၹݔᇿ3і4ᇏඔऌіൕਙэਈ൞ྛэਈ֥٤Granger
984॥ᇅંაႋႨֻ28जჰၹ֥pᆴ.২3ᇏݓܢ൧Grangerၹݔྟٳ༅.ᆃၛᇏݓܢ൧ቔູ࣮ؓའ,ॉҰധܢ൧ၛі3ॢగಙඔऌGrangerၹݔྟٳ༅pᆴࠣཐۖܢ൧ᆭࡗರ൬ၭੱ֥ၹݔܱ༢.ٳљ࿊౼ཌྷTable3Thep–valueofGrangercausalityanalysisႋ൧ӆ֥ᇶေᆷඔཐۖޚളᆷඔaഈᆣሸކᆷඔބforairpollutiondataധᆣӮٺᆷඔቔູ3۱ܢ൧֥սі.ဢЧ֥౼ᆴٓຶCONONO2O3GRI൞:2000୍1ᄅ3ರ֞2006୍12ᄅָ֥ૄರܢᆷ֥൬CO—ࡎ,ٳљ࠹ෘૌ֥ರ൬ၭੱrt:—=lnPt−lnPt−1,——ఃᇏPtູtರܢᆷ֥൬ࡎ,ѩؓఃࣉྛყԩ,—ఃਬनᆴ߄ބٚҵֆ໊߄.ٳљၛX1(t),X2(t)ބCO—(t)іൕყԩު֥ཐۖޚളᆷඔ൬ၭੱaഈᆣሸNO——ކᆷඔ൬ၭੱބധᆣӮٺᆷඔ൬ၭੱ,ࣜဒૌNO2———न൞໗ਙ.O3—————————Ֆ3ᇕܢ൧ᆷඔ൬ၭ(4∼6)ॖၛुԛ,ഈᆣሸކᆷඔ൬ၭੱބധᆣӮٺᆷඔ൬ၭੱ֥ѯ౦і4ॢగಙඔऌ֥ਆэਈGrangerၹݔٳ༅مpᆴྙࢠູཌྷර,طཐۖޚളᆷඔ൬ၭੱ֥ѯ౦ྙᄵTable4Thep–valueoftwo-variableGrangerބૌႵࢠູૼཁ֥ҵљ.০Ⴈభ૫۳ԛ֥ဒٚcausalityanalysismethodforairمॉҰ3۱ᆷඔᆭࡗ֥Grangerၹݔྟބࠧൈၹݔྟpollutiondata໙ี,ᇌުࢨඔ࿊౼k=5(۴ऌAICჰᄵ࿊౼),ջॺK=࿊౼ε7n=,ᇂߐဢЧ۱ඔB=199,ཁᇷྟඣα=,ૄᇕ౦ঃᇗگ1000Ց,ଆࢲݔі5.CONONO2O3GRIဒ෮֤3ᇕܢ൧ರ൬ၭੱၹݔೂ7(a)෮ൕ.CO—————4ഈᆣሸކᆷඔರ൬ၭ(a)ଆ෮֤Grangerၹݔ(b)ਆэਈGrangerٳ༅م෮֤Grangerၹݔ3ॢగಙඔऌGrangerၹݔ5ധᆣӮٺᆷඔರ൬ၭ
ֻ7௹້ᄃᗘ֩:ཟਈሱ݂߭ଆGrangerၹݔ่֥ࡱྐ༏я്აႋႨ985Վຓ,ഈݚܢ൧აധᎪܢ൧ರ൬ၭੱᆭࡗթᄝGrangerၹݔܱ༢,طധᎪܢ൧ཌྷؓႿഈݚܢ൧֥Grangerၹݔྟ۷ູૼཁ,ၹՎཌྷбႿࣇႨഈݚܢ൧֥ݖಀྐ༏ყҩఃໃটሼ൝,০Ⴈഈݚܢ൧ބധᆣܢ൧ݖಀ֥ྐ༏܋ყҩഈݚܢ൧ໃটэ߄൝ᄵି֤֞۷ູሙಒ֥ࢲݔ.ൈ,3ᇕܢ൧ರ൬ၭੱᆷඔࠧൈၹݔܱ༢ࢠ,ᆃඪૼଖ၂ܢ൧൬ၭੱ֥эᄝ؋௹ଽؓఃܢ൧൬ၭੱ֥႕ཙࢠཬ.6ཐۖޚളᆷඔರ൬ၭі6ᇏݓܢ൧֥ਆэਈGrangerၹݔٳ༅مpᆴ–valueoftwo-variableGrangerі5ᇏݓܢ൧Grangerၹݔྟٳ༅pᆴcausalityanalysismethodforChina’sTable5Thep–valueofGrangercausalityanalysisstockmarketforChina’sstockmarketK=5Ⴕཟшཟш(t)X2(t)X3(t)X1(t)X2(t)X3(t)(t)——(t)———(t)————5ࢲં(Conclusions)ᇿЧ໓࣮ਔ؟ົൈࡗਙ֥Grangerၹݔྟ؎4Ⴕཟш൞Ֆі5ᇏਙэਈᆷཟྛэਈ.໙ี.๙ݖؓ؟ົൈࡗਙGrangerၹݔ֥ࡹ৫,ࡼэਈࡗ֥Grangerၹݔྟ്љ໙ีሇ߄ູGrangerၹݔࢲܒ്֥љ໙ี.০Ⴈଆ෮ᄏݣ่֥ࡱ৫ྟሙᄵ,ܒࡹਔGrangerၹݔшթᄝაڎ֥ဒ࠹ਈ.ཌྷбႿԮ֥ਆэਈGrangerၹݔܱ༢ဒم,Ч໓෮۳֥ٚمି۷ሙಒّ֥ႋԛэਈࡗ֥(a)ଆ෮֤Grangerၹݔၹݔܱ༢,ൈ္ିّႋэਈࡗ֥ࠧൈၹݔܱ༢.Ч໓۳ԛ֥ଆٚمေડቀၹݔԉٳྟ่ࡱ,ᄝൌ࠽ܴҩᇏ,ࣜӈ߶Ⴕႅэਈ໙ีԛགྷ,ؓႿݣႅэਈ֥Grangerၹݔ໙ีႵրႿࣉ၂࣮҄.ҕॉ໓ང(References):[1]-(b)ਆэਈGrangerٳ༅م෮֤Grangerၹݔelsandcross-spectralmethods[[J].Econometrica,1969,37(3):424–ᇕܢᆷರ൬ၭੱGrangerၹݔ[2]KAMINSKIM,DINGZ,TRUCCOLOW,:Grangercausality,directedtransferfunc-stockindexdailyreturntionandstatisticalassessmentofsignificance[J].BiologicalCyber-Ⴎဒࢲݔॖᆩ,ཐۖܢ൧ؓഈݚܢ൧ၛࠣധnetics,2001,85(2):145–157.Ꭺܢ൧ರ൬ၭੱ֥႕ཙ٤ӈཬ.҂Ⴟ໓ང[17],ഈ[3]:GrangerCausalityanalysisonݚܢ൧ބധᎪܢ൧ᄵ൞ཐۖܢ൧ರ൬ၭੱэ߄֥ჰOECDcountrieswithapanelapproach[J].EconomicModelling,ၹ2006,23(6):978–992.,ᆃඪૼෛሢཐ֥݂ۖ߭ၛࠣࣜ࠶၂ุ߄൝֥ᇯࡶᄹ఼,ཐۖܢ൧ؓնܢ൧թᄝૼཁ֥၇ঠྟ[4]NAGARAJANR,[J].Bioinformatics,2008,ಖط,ਆэਈGrangerၹݔٳ༅م(ࢲݔі6,ཌྷႋ֥24(7):1029–1032.ၹݔ7(b))ᄵஆԢਔഈݚބധᎪܢ൧ؓཐۖܢ[5]ݒඣ༩.თ۬ধࢭၹݔܱ༢ࠣఃᄝྐݼԩᇏ֥ႋႨ[J].࠹ෘ൧֥႕ཙ.ࠏ۽ӱაႋႨ,2008,44(3):5–9.
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