1、VAR模型應用實例眾所周知，經(jīng)濟的發(fā)展運行離不開大量能源的消耗，尤其是在現(xiàn)代經(jīng)濟發(fā)展的過程中，能源的重要性日益提升。我國自改革開放以來，經(jīng)濟發(fā)展取得長足的進步，經(jīng)濟增長率一直處于較高的速度，經(jīng)濟的高速增長帶來了能源的大量消耗，進而帶來了我國能源生產(chǎn)的巨大提高。因此，研究經(jīng)濟增長率與能源生產(chǎn)增長率之間的關(guān)系具有重要的意義，能為生源生產(chǎn)提供一定的指導意義。1.基本的數(shù)據(jù)我們截取19782015年中國經(jīng)濟增長速度（GDP增速）和中國能源生產(chǎn)增長速度數(shù)據(jù),具體數(shù)據(jù)如下：表119782016年中國經(jīng)濟和能源生產(chǎn)增長率年份國內(nèi)生產(chǎn)總值增長速度（%）能源生產(chǎn)增長速度鮒年份國內(nèi)生產(chǎn)總值增長速度（%）能源生產(chǎn)增

2、長速度鮒197811.710.419979.20.319797.63.719987.8-2.719807.8-1.319997.71.619815.1-0.820008.55198295.620018.36.4198310.86.720029.16198415.29.220031014.1198513.49.9200410.115.619868.93200511.411.1198711.73.6200612.76.9198811.25200714.27.919894.26.120089.7519903.92.220099.43.119919.30.9201010.69.1199214.22.3

3、20119.59199313.93.620127.93.21994136.920137.82.21995118.720147.30.919969.93.120156.91.22.序列平穩(wěn)性檢驗（單位根檢驗）使用Eviews9.0來創(chuàng)建一個無約束的VAR模型，用gdp表示的是中國經(jīng)濟的增長率，用nysc表示中國能源生產(chǎn)的增長率，下面分別對gdp和nysc進行單位根檢驗，驗證序列是否平穩(wěn)，能否達到建立VAR模型的建模前提。墮S-eries:GDPWorkfile:UNTITLED:Untitle-d|匚i|回ViewProcObjectPropertiesPrintNameFreezeSample

4、GenrSheetGraphAugmeiiwdDick.ey-FullerUnitRootT&stonGDPNull咖阿血對GDPhas且unitrootExogenous:ConstantLagLength:3Automatic-basedonSIC,maxlag=9Augm朗柜dDick町-Fulleteststatistic；心.67忑53CI.U056Testcriticalvalues:1%level-3.639+075%level-2.95112510%level-2.6100*MacKinncn(1996)one-sidedp-valuesAugmentedDickey-Full

5、erTestEquationDependentVariable:DGDP)Method:LeastSquaresate:05J17/17Time:10:55Sample(adjusted:19022015Includedlobservations:34-afteradjustmEntaVariableCoefTicientSid.Errort-StatisticProb.GDP(-1-08551710.221114-3.B6755J0.00Q6DCGDP-1)0.5256310.1935293.2327550.0031D(GDP(-2)004924001755170.28054407811D(

6、GDP(-3)02049370.1673401.5831450.1242C3.MOO502.2229613.S417450.0006R-squared0.453475Meandependentvar0.052941AdjustedR-squared0_3837tt2S.D.dependentwar2545731戸Li-bfrrnkrirr*cc；cin/liIrrmiImIcirrifirnJ圖21經(jīng)濟增速（GDP）的單位根檢驗0SeriesNY&CW&rkfle:UNTITLED：!UntitledViewProcObjectPropertiesPrintNameFreeze1Sample-

7、GenrStieetjcraphAugmentedDick&y-FullerUnitR.ootTestonNYSCNullHypothesis:NYSChasaunitrootExogenous:ConstantLagLength:1CAutorratic-basedonSIC,maj(lag=9t-StatisticProb百1覽171總朮的口酣時孑111俺愴皿甜5血-3衛(wèi)35937CLOO45Testcriiicalvalues:1%level-3.6267045%level-2.94&04210%level-2.6115S1MacKinnon(1996)one-sidedp-values

8、AugmentedDie：key-FuIlerTestEquationDependentvariable:D(MYSC)Method:LeastSquaresDate:05/17/17Time:10:&8Sampleadjusted):19802015-Includedobsen/atiori5：36afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.NYSC-1)-0.5309060.134905-3.9359870.0M4(NY3C(-1M0.4385490.1500552.9225050.0062C27469330.S5

9、72663.2043000.0030R-squared0.M306SMeandependentvar-0.0694UAdjustedR-squared0.303254SO.dependentvar3.51070iS.E.ofregression2930431Akaikeinfocriterion5.067831Sumsquaredresid283.3851Schwarzcriterion5.199791Loglivelihood-S3.22Q96Hannan-Quinncriter.5.1133S9F-statisticS.616746Durbin-Watsonstat1.99Q251Prob

10、(F-stati-stic)C.Q00975圖22能源生產(chǎn)增速（nysc）的單位根檢驗經(jīng)過檢驗，在1%的顯著性水平上，gdp和nysc兩個時間序列都是平穩(wěn)的，符合建模的條件，我們建立一個無約束的VAR模型。3.VAR模型的估計ProcObjectPrintNameFreezeEstimateFarecastVectorAutoregressionEstimatesVectorAutoregressionEstimatesDate:05/17/17TimeiltOGSampleadjusted:19802015Includedobservations:36afteradjustmentsStan

11、darderrorsin()&t-statisticsinGDPMSCGDP(-1)0.82S&44(0.164995.003690.271598(0.23599)1.15056GDP(-2)-0.53049&(0.16625-3.19096-0.292356(0.237S0；-1.22942NYSCC-1-0.05222&(C115B5-0.451560.846356(016543)5.11612NYSCC-2)0.186100011349)1.63977-0.35756S(0.16234)-2.20263C6.194518(1.508874.105392.863291(2.15827132

12、666R-squared0.4925650.&4387Adj.R-squared0.427089049GSSSS-umsq.reside1305151267.0323SEequation2.051S692.924958F-.statistic7.522S909.641791Loglikelihood-74.2652&-37-15117AkaikeA1C4.4026255.119509S-chwarzSC4.62J5585.339442Meandependent9.7383395.016667SD.dependent2.7108544.1J7a5Determinantre.sidcovarian

13、ce(dofadj.)30.72390Determinantre.sidcovariance22.78215Loglikelihood-158412AkzaiIceinformationcriterion9.3-57237Schwarzcriterion9.797154圖3.1模型的估計結(jié)果回丫盯;VAR01Workfile-;完成的VARSH：:Untitled1=1叵基ViewProcObjectPrintName|Freeze|EstirnatEForecastSizatsImpijlseResidsI.tian.FrocLS12GDFN1!SCmModel:GDP=C(l,1&DP(-

14、O+E刃宋GDP(-2)+CCl.SnSCf-l)+C(l,4)*1IVSC(-2)+C(l.E)UYSC=Ct2,l)*GBP(-10+C(Z2)*GDP(-2)+Ct2,3)*ISC(-1)+C(2,4)*NVSC(-2)+HZ引7AIiMedel-SubstitutedCoeffi?ints:GDT=0.S25544312S35*(5Dr(-l)-0.5304S4707434*?Dr(-2)-0.Q522E47C95102lTYSC(-1)+0.1861004S07E4tMSC(-2)+6.19451824763KY匯=Cl.E門59陽3葩T4WGDF(T)-.292356168154B

15、FC-250.84635586S747ffYSC(-1)-0.357567632748*SSC(-2)+2.86329108178圖32模型的表達式4.模型的檢驗4.1模型的平穩(wěn)性檢驗回Var:UNTITLEDWorldile:UMTrTLED:Umitle(AViewProcObjectPrintN目rntFreezeLstimateForecastSIVARStabiLityCondLtior)Ch&ckRootsofCharaderisticPolynomialEndogenousvariables:GDPNYSCExogenousvariables:CLagspecification:

16、12ate:05/17/17Time:11:11RootModulus0566086-0.451708iC-.7242200566086+0.451708iC,7242200.269864-0.626551i0.632-1960.269864+0.626551i0.632196Norootliesoutsidetheunitcircle.VARsatisfiesthestabilitycondition圖4.1.1AR根的表由圖4.1.1知，AR所有單位根的模都是小于1的，因此估計的模型滿足穩(wěn)定性的條件。1.00.00.00.51.01.5InverseRootsofARCharacteris

17、ticPolynomial圖4.1.2AR根的圖通過對GDP增長率和能源生產(chǎn)增長率進進行了VAR模型估計,并采用AR根估計的方法對VAR模型估計的結(jié)果進行平穩(wěn)性檢驗。AR根估計是基于這樣一種原理的:如果VAR模型所有根模的倒數(shù)都小于1,即都在單位圓內(nèi),則該模型是穩(wěn)定的;如果VAR模型所有根模的倒數(shù)都大于1,即都在單位圓外,則該模型是不穩(wěn)定的。由圖4.1.2可知,沒有根是在單位圓之外的，估計的VAR模型滿足穩(wěn)定性的條件。4.2Granger因果檢驗Var:VAR-01Workfile:EE&lVAR-IKSl:Untitled|=|ViewProrObjectPrintNameFreezeIEs

18、timateForeicastStatsImpuliVARGrangerCausality/BlockEx口eneityWaldTestsate:05/19/17Time:zo：5Tsample:197B2aT5Includldlobssrvstion占：36Dependlent即aiiJiablE：GDPEciuaedoni-sqCJTPrat)NSC3.03869320.2189All3.0396982a.2103Dependsrrt釘NYSCExcludedChi-sqdfProb.GDP1.6932612a.3871All1.89828120.3871圖4.2.1Granger因果檢驗

19、結(jié)果圖Granger因果檢驗的原假設(shè)是：H0：變量x不能Granger引起變量y備擇假設(shè)是：%：變量x能Granger引起變量y對VAR（2）進行Granger因果檢驗在1%的顯著性水平之下，經(jīng)濟增速（GDP）能夠Granger引起能源生產(chǎn)增速（NYSC）的變化，即拒絕了原假設(shè)；同時，能源生產(chǎn)增速（NYSC）能夠Granger經(jīng)濟增速（GDP）的變化，即拒絕了原假設(shè)，接受備擇假設(shè)。5滯后期長度回Var:UNTITLEDWorkfila:UNTITLED:UntitladviewProcObjectPrintNameFreezeEstimateForecastStatsImpulseReslds

20、ZoomVARLagOrderSelectionCriteriaEndocenousvaria&les:GDPNYSCExogenousvariables:3ate:D5/17/17Time:1116Sample:197S2015Indudedobservaticns:34LagLogLLRFPEAICSCHQ0-172.74-23NA99.3069610.2789610.36B7410.309531-158.855025.S239455341499.6973519.9667099.7892102-148.079713312737.6133indicateslagorderselectedby

21、thecriterionLR.sequentialmodfiedLRleststatislic（eachtestat5%levelFPE:FinpredictionerrorA1C:kaieinformationcriterionSC:SchwarzinformationcriterionHQ:Haman-Quinninfornationcriterii圖5.1VAR模型滯后期選擇結(jié)果從上圖可以看出LR,FPE,AIC,SC,HQ都指向同樣的2階滯后期，因此應該選擇VAR（2）進行后續(xù)的分析。9.293806*9.747733*9.451906*3-147.4983D.92353446.343

22、659.49989710.12B40B.7142344-145.49842.9W91652S58SB9.61755510.425639.8931316.脈沖函數(shù)圖6.1各因素脈沖響應函數(shù)結(jié)果圖從圖6.1可以看出：經(jīng)濟增長率（GDP）和能源生產(chǎn)（NYSC）各自對于自身的沖擊，在前四期是快速下降的趨勢，并且出現(xiàn)負值的情況。但是，GDP增速的變化基本上在第七期就保持了持平的一個狀況；而能源生產(chǎn)（NYSC）的變化是在第九期的時候?qū)崿F(xiàn)持平的狀態(tài)。能源生產(chǎn)增長率（NYSC）對于經(jīng)濟增長率（GDP）的脈沖響應分析，當給經(jīng)濟增長一個正的沖擊的時候，在前兩期是呈現(xiàn)一個下降的趨勢，主要的原因應該是，經(jīng)濟增長促進能

23、源生產(chǎn)的提高是存在滯后期的，但是但很快就出現(xiàn)了上升的趨勢在第五期的時候達到最大值，之后出現(xiàn)了下降的趨勢，然后又回升，直到第十期之后保持了平衡。這說明經(jīng)濟增長對于能源生產(chǎn)增長的影響是正向的，會呈現(xiàn)一種上升、下降、平衡的基本狀態(tài)，說明經(jīng)濟發(fā)展對能源生產(chǎn)的促進作用并不是無限的，經(jīng)過一定作用之后看，會出現(xiàn)一種平衡狀態(tài)。經(jīng)濟增長率（GDP）對于能源生產(chǎn)增長率（NYSC）的脈沖響應分析，經(jīng)過對比圖中第2幅和第3幅小圖，我們大致是可以看出兩者之間是呈現(xiàn)完全相反的情況。當在本期給能源生產(chǎn)增長率（NYSC）個正沖擊之后，前兩期是增長，然后到第五期是下降趨勢，然后回升，在第七期之后基本上持平。7.方差分析畫Var

24、:UNTITLEDWorkfile:UMTm_ED:UnMI&d|回ViewProcObjectPrintNameFreezeEstimateJFareca&tSttsImpulseResideZoomVarianceD&cjormpositionVarianceDecompositionofGDP:PeriodS.E.GDP忖紀12.051869100.00000.00000022.62678299.711540.28045832.66955398.721431.2785-704-2.76860692.919477.030533-52.84515359.1101110.3893962.851

25、17158.8871311.1120712.B58S27S8.43C0711.56993Q2.S7241057.6373412.3-626692.876777a?4049012.595-10102.876820a?4023112.59769112.877548B7.3871112.B1289122.87829637.3730712.6269S132878481373670712.6329U2.S7352537365091Z63491152.S7S57S87365OS12.634-92162.S7S601573652412.634-76172.S7S613573646612635-34is2.S

26、7362557.3639212.636OS192.878629573636812.63632202.878630573636912.63631212.878631573636412.63636222.878632573635812.63642232.878633573635612.63644-242.878633573635612.63644-252.878633573635612.6364+26Z.S786337.3635612.63644-27Z878633B7.3635612.63644-23Z8786337.3635612.63644-292.878633873635612.636U3

27、02.87863387363561Z63644圖71經(jīng)濟增長（GDP）方差分析結(jié)果回VanUNTfTLEDWorkfile:UNTfTLED:UntitledViewProcObjectPrintNameFreezeLstimateForecastSUtsImpulseResidsZoomVarianceDe-compositionVarianceDeccimpositionofNYS-C:PeriodS.E.GDPNY&C12.934958152S24284.7175824-.02209122.5767677.4232434-.19194823.7934076.2065244-.20S62924.176517S.-82349542K1S426.2479S73.75205642S8S7527.14570Z2.-8&43074.30702327.0992872.9007284.31470027.0676472.9376g431S40127.1087872.-S932410431S99627.1252272.-8747-S114.32022527.1145572.-8S&451227.1025772.-S974S134-32146327.0999472.90006U4321