状态空间模型在经济预测方面的应用研究

130012ARIMAGDPM1ARIMA:F224.0A()[1]1Tiao&Hillmer1978[2]ARYoung&DukARIMA[3]ARIMAARIMA12Luenberger[4]Harvey[5]West&Harrison[6]tttvXFY+='(1a)tttwGXX+=−1(1b){{{{G}tv}tw}tY}tXnF{O(1a)(1b)}tYn0X0110)]'(,),(),([OXYEYEYEn=−K(2)]')'(,,',[1FGFGFOn−=K{(1)}tY0XOn[7]3ARIMA3.1ARIMA(1,1,1)ARIMA(1,1,1),TCTCAR(1)tYttYttItItttITCY+=(3a)ttwTCL=−)1((3b)ttvIB=−)1(φ(3c)L1)(−=ttTCTCL),0(~2wtNwσ),0(~2vtNvσ=tttITCY)11((4a)+=−−ttttttvwITCITC11001φ(4b)),0(~ΩNvwtt(3a,3b)(3a)tY)1)(1(LL−−φtttILLTCLLYLL)1)(1()1)(1()1)(1(−−+−−=−−φφφttvLwL)1()1(−+−=φtLεθ)1(−=tttvLLwLLθθφε−−+−−=1111YARIMA(1,1,1)ARIMA(1,1,1)t23.2ARIMA(p,d,q)YARIMA(p,d,q)YTCAR(p)tttttITCdtItYtttITCY+=(5a)ttdwTCL=−)1((5b)ttppvILLL=−−−−)1(221φφφL(5c)(5a)dppLLLL)1)(1(221−−−−−φφφLtqqtdppLLLYLLLLεθθθφφφ)1()1)(1(221221−−−−=−−−−−LL(6)tεq(6)YARIMA(p,d,q)(5a~5c)ARIMA(p,d,q)),max(dp=t3.3ARIMA{{ARIMA(1,1,1)}tY}tYttLYLLεθφ)1()1)(1(−=−−,(7)),0(~2εσεNtφARIMA()ttXY11=(8a)+=−ttttvwXX1001φ(8b)),0(~ΩNvwtt(′=tttITCX)φAR(1)Ω{{ARIMA(1,2,1)(9a)}tYtTC=}tYttIY+ttwTCL=−2)1((9b)ttvIL=−)1(φ(9c)ttXY)101(=(10a)+−=−ttttvwXX0000010121φ(10b)),0(~ΩNvwtt(′=−ttttITCTCX1)φAR(1)ΩARIMAAR(1)AR(p)ARIMA(p,d,q)33.4(1)(2)ARIMA(3)ARIMA(4)ARIMA(5)Kalman(6)4KalmanKalmantKalmanKalman4.1GDPGDP1995120014()199512000420011~4GDPX-11,GDP_TCIGDPGDP_S2000420014GDP_TCIARIMA(1,1,1)GDP_TCIttYLLε)48.01()08.447)1)((15.01(−=−−−(11)GDP_TCI()=ttttIbTCY101(12a)+=−−−ttttttttvwIbTCIbTC015.000010011111(12b)TCAR(1)(2)(12a,12b)Ot1=−tItwtv08.4470===bbbttL7225.0=OO4800012000160002000024000280003200019951996199719981999200020011GDP()()GDP_TCIGDP11GDP120011~4GDPGDP20011~42.67%67.2=MSTR4.2M1()()2M119951~2001419951~2000420001~4219951~20011219951~20001220001~1213.1=LSMSTRARIMA09.21=MMSTR10001500200025003000350040004500199519961997199819992000200120000300004000050000600007000019951996199719981999200020012()()3M1()()5ARIMAGDPGDP19951~2001419951~20005420011~44580001200016000200002400028000320001995199619971998199920002001800012000160002000024000280003200019951996199719981999200020014GDP()5GDP()()()145MSTR120011~4GDP120011200122001320014MSTR19895.0023047.0024285.0028706.1019254.4822302.2923797.1428860.182.6719059.3022311.7923567.1529369.323.0621391.6623851.6825728.2129761.115.091GDPMSTR6ARIMA,6ARIMA[1].[M].,1998,p434.[2]Tiao,G.C.andHillmer,S.C.,“Someconsiderationofdecompositionofatimeseries”,[J].Biometrika,65(1978),497-502.[3]YoungJinJooandDukBinJun,StatespaceTrend-cycleDecompositionoftheARIMA(1,1,1)process[J].JournalForecasting,VOL.16,411-424,1997.[4]Luenberger,D.G.IntroductiontoDynamicSystems:Theory,Models,andApplications[M].NewYork:JohnWiley,1979.[5]Harvey,A.C.ForecastingstructuraltimeseriesmodelsandtheKalmenfilter[M].CambridgeUniversityPress,1989,Chapter3,101-167.[6]West,M.andHarrison,J.BayesianForecastingandDynamicModels[M].Berlin:Springer-Verlag,1989.[7]Aoki,M.,“TwoComplementaryRepresentationsofMultipleTimeSeriesinState-SpaceInnovationForms[J].JournalofForecasting,1994,69-90.TheapplicationstudyineconomicforecastoftheStateSpaceModelGAOTie-mei,CHENFeiCenterforQuantitativeEconomics,JilinUniversity,JilinChangchun,130012ChinaAbstractThispaperdiscussesequivalencerelationshipsbetweentheARIMAprocessandtheStateSpaceModelandsetupproperStateSpaceModels.China’seconomictimeseriessuchasGDP,M1andtotalretailsaleofconsumergoodsareusedtosetuptheStateSpaceModels.AndthepaperforecaststimeseriesbyusingStateSpaceModels.TheresultsderivedinthispapershowthattheStateSpaceModelhasobtainedgoodforecastresults,anditprovidesaneweffectivewayforeconomictimeseriesforecasting.KeywordsStateSpaceModel;ARIMAprocess;Controllability;Forecast2003-5-29(01JAZJD790003)(1951-)(1973-)7