中国货币需求波动研究_广义可塑最小二乘法及其推广

——广义可塑最小二乘法及其推广刘　勤　顾　岚ABSTRACTAnewmethodofparametersestimation-GeneralizedFlexibleLeastSquares(GFLS)wasintroduced,thenthismethodwastriedtobeextended,andfinallytheanalysisonChinasmoneydemandwasmadebyusingthismethod.一、引言?,M=f(Y,P,r)(1)M,Y,P,r,,,KalabaTesfatsion1989FLS(FlexibleLeastSquares)Ltkepolh(1994),1996FLSGFLS,,,GFLS,L1:,,,:(),(OLS),,,,,,,,GFLS,,,GFLS,,GFLSBayes,,GFLS二、货币需求函数(1),,,,M1,,GDP,GDP,,,60StatisticalResearch19983No.31998()PM1P,,,,,3(3),,,,,,19853,1981-1996,M1,GDP,P3r,:mt=1gdpt+2rst+3pt(2)mt=ln(Mlt/Pt),gdpt=ln(GDPt/Pt),pt=lnPt,rst=ln(a+rt),rt,(2),,,,,HendryRichard(1983):mt=v0+v1(mt-1-1gdpt-1-2rst-1-3pt-1)+1gdpt+2rst+3pt+!t(3),!t,(3),,三、GFLS方法1.GFLSGFLS,,yt=xt∀t+tt=1,2,,T(4),ytM1(),xt=(xt1,,xtK)MK(),∀t=(∀t1,,∀tk)K1GFLS:Q(∀)=Tt=1(yt-xt∀t)Ht(yt-xt∀t)+#1Tt=2(∀t-∀t-1)Dt(∀t-∀t-1)+#2Tt=S+1(∀-∀t-S)Ft(∀t-∀t-2)(5)Ht,Dt,FtKK,,#1#2,s,s=4GFLS(5)∀1,,∀T(5)3r2M(∀,∃),r2D(∀,T)r2s(∀,∃),T:R(T)={r2M(∀,∃),r2D(∀,∃),r2s(∀,∃)∀ENK}R(T)y1,y2,,yT,TR(T)E3(r2M,r2D,r2s),T,RF(T)T,,GFLS(5)Dt,Ft,r2Dr2S,,,(),(#2=0),Q1(#1)=r2M(∀,∃)+#1r2D(∀,∃)FLS,#1,FLS,#10,,(#1=0),Q2(#2)=r2M(∀,∃)+#2r2s(∀,∃),#2,,#261:0,,,OLS,,OLS,OLSFLS,OLS,(r2D,r2s),FLSGFLS,,S,GFLS2.GFLSGFLS(5),:Q(∀)=yHy-2yHX∀+∀(XHX+G)∀y=y1yTTM1,H=H100HTTMTM,X=x100xTTMTK,∀=∀1∀TT%1G=#1E1DE1+#2EsFEsD=D100DT,F=F100FT,E1=0-II0-II0-IIEs=0000000-I00I0-I00ID,F,E1EsTKTK,∀,∀(XHX+G)∀=XHy(6)∀A=XHX+G,AHt,Dt,Ft,,ADt,Ft,Dii=Gii=1TTt=1x2tiDt,Ft∀x,,Ht3.GFLSGFLS,,,HtGFLS,,,,,L1,HtHt=&t100&tM&ti=1,1yti-y~ti,yti-y~ti10-5yti-y~ti10-5(8):1y~tiHtFLStyti,∀;2,(8)Ht,,∀;3,,,　　四、GFLS实证分析,yt=mt,62xt=(1,mt-1,gdpt-1,rst-1,pt-1,gdpt,rst,pt)∀t=(∋0t,∋1t,-∋1t1t,-∋1t2t,-∋1t3t,1t,2t,2t)∀t,it:it=∋itit/∋~1t#,#i=0,0.001,1,1000(i=1,2)16,,,,F,D,diiTt=1x2ti/T,,,,1,,,(),,,,,:1.,Q2(#2),Q1(#1)2.,Q2(#2),Q1(#1),3.,Q1(#1),Q2(#2)4.Q3(#1,#2),#1,#2,1,2,3,Q1(#1),Q2(#2),4,#2,SSE#1,,#1,SSE#1,,SSE#1#2,,,#i(i=1,2),,,#i(i=1,2),,,#1,#20,0.001,1,1000,,,1#(a)#1=0.001#2=0(b)#1=1000#2=0(c)#1=0#2=0.001(d)#1=0#2=1000Q1(#1),Q2(#2),Q3(#1,#2),(1)(8)∋0,∋1,1,2,3,1,2,3,(a),(b):∋0,∋1;1,1988,GDPM12(a)1986,(b),3,(a),19891993,,(b),19891992,,,,,19932,3,,M1,,,1,2,3,,,(c),(d),∋0,∋1,1,2,3;1,22(b),(d),,(#2=1000),(b)(d),,63:,1,#1,#2,2,3,,64,,,GFLS,::mt:1981219964t-0.870870.2763000-3.150156mt-1-0.0339510.039000-0.870539gdpt-10.3240940.0443687.304758rst-1-0.0075100.014564-0.515667pt-1-0.2336930.077891-3.000264gdpt0.1610730.0219697.331746rst-0.0702350.035442-1.981680pt-0.317260.177510-1.789293R2=0.546168D.W.=1.638565R-2=0.488408AIC=-6.340843SSR=0.039577F=9.455763,,OLS,CUSUM-R0.05,GFLS,CUSUM-R,,,GFLS,GFLS,五、小结GFLS,,,GFLS,19811996,,,GDP,,,,GFLS,[1]KolabaR,TesfatsionL(1989)Time-varyinglin-earregressionviaflexibleleastsquares.Comput-ersandMathematicswithApplications17:1215-1245[2]KalabaR,TesfatsionL(1990)FlexibleleastsquaresforapproximatelyLinearsystems.IEEETransactionsonSystems,Man,andCy-berneticsSMC-290,978-989[3]LtkepohlH(1994),TheSourcesoftheU.S.MoneyDemandInstability.NewDevelopmentsinTimeSeriesEconomtrics,Physica-VenlagHeidelberg,173-187[4]LtkepohlH,HerwartzH(1996),Specificationofvaryingcoefficienttimeseriesmodelsviagener-alizedflexibleleastsquares.JournalofE-conomtrics70:261-290[5]TesfatsionL,VeitchJ(1990)USmoneydemandinstability:Aflexibleleastsquaresapproach.JournalofEconomicDynamicsandControl14:151-173:刘勤,1990年毕业于陕西财经学院统计系,获硕士学位,现为中国人民大学统计系博士生。顾岚,中国人民大学统计系教授。(责任编辑:石庆焱)65: