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[24]7.17.1()xtyyt7.2()Dynamicmodels7.3()DistributedlagmodelstemporalcorrelationstochasticprocesstimeseriesprocessrealizationfinitedistributedlagFDLmodelyt=®0+±0zt+±1zt¡1+¢¢¢+±qzt¡q+ut²²7.1(TS.1)7.2(TS.2)tutstrictlyexogenousy.7.4()contemporaneouslyexogenousE(utjxt)=07.3(TS.3)7.1(OLS)TS.1-3XtOLS7.4(TS.4)XtuttVar(utjXt)=Var(ut)=¾2-119-7.17.5(TS.5)XCorr(ut;usjX)=07.2(OLS){TS.1-5^¯jXVar(^¯jjX)=¾2=[SSTj(1¡R2j)]7.3(^¾2)TS.1-5^¾2=SSR=(n¡k¡1)¾27.4({)TS.1-5XOLS7.6(TS.6)utXi:i:d:TS:3¡57.5()CLMTS:1¡6XOLSttFF7.5()eventstudyyt=®0+®1t+et(7-1)½E(yt)=®0+®1tVar(yt)=Var(et)=¾27.6()exponentialtrend:log(yt)=¯0+¯1t+etOLSTS:27.7()covariancestationary-120-²E(xt)²Var(xt)²th6=1Corr(xt;xt+h)ht(realization)7.8()weaklydependentxtxt+hhhxtxt+hLLNCLT7.9()h!1Corr(xt;xt+h)!0asymptoticallyuncorrelated7.10(AR(1))AR(1){stabilityconditionj½j1yt=½yt¡1+etstableAR(1)processCorr(yt;yt+h)=½h(7-2)7.11()trend¡stationaryprocess7.6(OLS)OLSplim^¯j=¯jOLS7.7OLSOLStFLMOLSinft¡inf¤t=¯1(unem¡¹0)+et(7-3)-121-7.17.12()cyclicalunemployment7.13()unanticipatedinflation7.14()etsupplyshock¯10adaptiveexpectationOlS7.15()highlypersistentorstronglydependent{yyyCLMintegratedoforderzeroI(0)integratedoforderfirstI(1)AR(2):½2¡1;½2¡½11;½1+½2=1²¹(t)=EfYtg²°(t;s)=Cov(Yt;Ys)²½(t;s)=Corr(Yt;Ys)=°(t;s)=p(°(t;t)°(s;s)²Á(t;s)=CorrfYt;YsjYs+1;¢¢¢;Yt¡1(lagoperator)L:LkYt=Yt¡kdifferenceoperation:±dYt=±(±d¡1Yt)=dX0(¡1)jCjdYt¡j7.16()7.17()-122-7.1AR(1)1DATATEMP(KEEP=Y1¡Y50);2ARRAYYY1¡Y50;3Y(1)=RANNOR(¡1);4DOJ=2TO50;5Y(J)=SQRT(0.5)¤Y(J¡1)+SQRT(0.5)¤RANNOR(¡1);6END;7RUN;PROCTRANSPORTOUT=TEMP;RUN;DATATEMP;8SETTEMP;910PROCARIMADATA=TEMP;11IDENTIFYVAR=COL1NLAG=6;12RUN;1314PROCARIMADATA=TEMP;15IDENTIFYVAR=COL1NLAG=6;16RUN;1718IDENTIFYVAR=COL1(1)NLAG=6;19RUN;20ESTIMATEP=1;21RUN;22ESTIMATEP=1Q=1;23RUN;24FORECASTLEAD=6OUT=FORECAST;25RUN;26IDENTIFYVAR=COL1(1,1);/¤second¡di®erence¤/27RUN;ARIMADATAPROCENDSASQUITWt=¹+µ(B)Á(B)tWt=(1¡B)d(1¡Bs)DYtsconstant=Á(B)¹7.18()f(k)(tailso®)f(k)®10;®20jf(k)j®1e¡®2kk=0;1;¢¢¢f(k)p(cuttso®)kpf(k)=0-123-7.2²²(stationary)()t;F;Â2(spurious)(cointegration)(autoregressiveintegratedmovingaverage)Box¡JenkinsARIMA7.2^¯j^¯jE(utjxt)=9^¯j¯j:AR(1)E(etjut¡1;ut¡2;:::)=0Var(etjut¡1)=Var(et)=¾2eAR(1)(1)OLS^ut¡1t=1;2;¢¢¢;n(2)^ut^ut¡1t=2;3;¢¢¢;n^½t(3)H0:½=0H1:½6=0DurinandWatson;1950DWDW=nPt=2(^ut¡^ut¡1)2nPt=1^u2tDW¼2(1¡^½)-124-H1:½02DW(1)OLS^utt=1;2;¢¢¢;n(2)ut^ut¡1t=2;3;¢¢¢;n^ut¡1^½t(3)LMLM=(n¡q)R2^uFBreush¡GodfreytestAR(1)ut=½ut¡1+ett=1;2;:::utVar(ut)=¾2e1¡½2yt¡½yt¡1=(1¡½)¯0+¯1(xt¡xt¡1)+ett¸2¹yt=(1¡½)¯0+¯1¹xt+ett¸2quasi¡differenceddataAR(1)GLS:(1)OLS^ut(2)^ut^ut¡1^½(3)OLS^½½GLSet^¯1{serialcorrelation¡robuststandarderror(1)OLSyt=¯0+¯1xt1+¢¢¢+¯kxtk+ut;t=1;2;¢¢¢;nOLSse(^¯1)^¾OLSf^ut;t=1;¢¢¢;ng(2)xt1=±0+±2xt2+¢¢¢+±kxtk+rtf^rt:t=1;2;¢¢¢;ng^®t=^rt^ut(t)(3)g^v=nPt=1^®2t+2nPh=1[1¡h/(g+1)]ÃnPt=h+1^®t^®t¡h!^v(4)seSCR=[se(^beta1)=^¾]2p^v^¯j-125-7.37.3:y1;y2;¢¢¢;yn^yt=yt+yt¡1+¢¢¢+yt¡N+1N^ytw=a0yt+a1yt¡1+¢¢¢+aN¡1yt¡N+1NN¡1Pi=0aiN=1^^yt=^yt+^yt¡1+¢¢¢+^yt¡N+1N^yt=^yt¡1+®(yt¡1¡^yt¡1)^yt=®yt¡1+(1¡®)^yt¡1ARMA(AR)(MA)yt='1yt¡1+'2yt¡2+¢¢¢+'pyt¡p+¹tyt='1Byt+'2B2yt+¢¢¢+'pBpyt+¹t'(B)=(1¡'1B¡'2B2¡¢¢¢¡'pBp)'(B)yt=¹tyt=¹t¡µ1¹t¡1¡µ2¹t¡2¡¢¢¢¡µq¹t¡qyt=µ(B)¹tyt='1yt¡1+'2yt¡2+¢¢¢+'pyt¡p+¹t¡µ1¹t¡1¡µ2¹t¡2¡¢¢¢¡µq¹t¡q'(B)yt=µ(B)¹t-126-7.4DFxt=½xt¡1+t½xt½ttDicky¡¡Fuller1976DF1220ADFDFt½¡1Dicky¡¡Fuller;1970;1980:²¢xt=(½¡1)xt¡1+pXi=1µi¢xt¡i+t²¢xt=®+(½¡1)xt¡1+pXi=1µi¢xt¡i+t²¢xt=®+¯t+(½¡1)xt¡1+pXi=1µi¢xt¡i+t(1)H0:½=1ADF¿½½¡1t¿½½¡1tt(2)½=1¯(3)tH0:½=1-127-7.5cointegration7.1(GDPADF)ADFGDP7.2GDPADF1datatemp;2retainyear1977;3setgdp;45d1=dif1(gdp);6d2=dif2(gdp);78l1=lag(gdp);9l2=lag(d1);1011d3=dif(l1);1213year+1;1415output;1617title'OriginalSeriesGDP';1819procregdata=temp;20m0:modeld1=l1/nointdw;21m1:modeld1=l1/dw;22m2:modeld1=yearl1/dw;23mw:modeld1=yearl1d3/dw;24run;2526title'Di®erenceSeriesGDP';procregdata=temp;27md1:modeld2=l2/nointdw;28md2:modeld2=l2/dw;29run;7.5cointegration7.19()Xit;X2t;¢¢¢;Xktd®=(®1;®2;¢¢¢;®k)Zt=®Xt»I(d¡b)(d;b)Xt»CI(d;b)®7.2()YtCt-128-Yt=®+¯Ct+utCtStSt=®+¯Ct+ut[1]7.1(EG)Engle¡¡GrangerEngleGranger1987EGYt=®Xt+t^e=Yt¡^Yt^eYtXtYtXtI(2;1)¢¢¢Engle&Granger1987(A)DFJohansenJohansen1988Juselius19907.2(CRDW)Sargan&Granger(1983)DurbinWatsonCRDW;cointegratingregressionDurbinWatsontestH0:d=0DWCRDW7.3(EG&CRDW)OLS(1978¡2002)EGCRDW-129-7.67.3EG&CRDW1title'CalculateOLSResidualsofCosumingRegressingonGDP';proc2regdata=LI.cosgdp;3CGDP:modelcosuming=gdp/dw;4outputout=abcresidual=r;5run;datatemp;6setabc;7dr=dif(r);8lr=lag(r);9output;10title'Engle¡GrangerTest';procregdata=temp;11EG:modeldr=lr/noint;12run;7.6AR(p)AR(1)AR(2)xt=Á1xt¡1+Á2xt¡2+¢¢¢+Ápxt¡p+ut(7-4)(1¡Á1L¡Á2L2¡¢¢¢¡ÁpLp)xt=Á(L)xt=ut(7-5)Á(L)7.11AR(p)?AR(1)xt=Á1xt¡1+ut(7-6)11¡Á21¾2u8:xt=(1¡Á1L)¡1ut=11+Á1L+(Á1L)2+¢¢¢utAR(2)xt=Á1xt¡1+Á2xt¡2+ut(7-7)8:Á1+Á21¡Á1+Á21Á21-130-7.2(AR(2))²(??)²²(Á1;Á2)pXi=1Ái1AR(p)AM(q)xt=ut+µ1ut¡1+µ2ut¡2+¢¢¢+µqut¡q(7-8)£(L)=(1+µ1L+¢¢¢+µqLq)=01xt=Á1xt¡1+Á2xt¡2+¢¢¢+Ápxt¡put+µ1ut¡1+µ2ut¡2+¢¢¢+µqut¡q+ut(7-9)©(L)xt=£(L)ut7-1AR(2)-131-7.7-4-202420406080100120140160180200ARMA7-2ARMA(1,1)7.20()7.21()dd©(L)¢dyt=£(L)ut(7-10)¢dyt=xtyt=Sdx