VAR模型應(yīng)用案例完成

1、VAR模型應(yīng)用實(shí)例眾所周知，經(jīng)濟(jì)的發(fā)展運(yùn)行離不開大量能源的消耗，尤其是在現(xiàn)代經(jīng)濟(jì)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(jì)發(fā)展取得長足的進(jìn)步，經(jīng)濟(jì)增長率一直 處于較高的速度，經(jīng)濟(jì)的高速增長帶來了能源的大量消耗，進(jìn)而帶來了我國能源生產(chǎn)的巨大提高。因此，研究經(jīng)濟(jì)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(dǎo)意義。1.基本的數(shù)據(jù)我們截取19782015年中國經(jīng)濟(jì)增長速度（GDP曽速）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1 1978 2016年中國經(jīng)濟(jì)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（%年份國內(nèi)生產(chǎn)總值增 長速度（

2、%能源生產(chǎn)增長速 度（%197811.710.419979.20.319797.63.719987.8-2.719807.8-1.319997.71.619815.1-0.820008.55198295.620018.36.4198310.86.720029.16198415.29.220031014.1198513.49.9200410.115.619868.93200511.411.1198711.73.6200612.76.9198811.25200714.27.919894.25.120089.7519903.92.220099.43.119919.30.9201010.69.1199

3、214.22.320119.59199313.93.620127.93.21994136.920137.82.21995118.720147.30.919969.93.120156.91.22.序列平穩(wěn)性檢驗(yàn)（單位根檢驗(yàn)）使用Eviews9.0來創(chuàng)建一個(gè)無約束的 VAR模型，用gdp表示的是中國經(jīng)濟(jì)的增長率，用nysc表示中國能源生產(chǎn)的增長率，下面分別對(duì)gdp和nysc進(jìn)行單位根檢驗(yàn)，驗(yàn)證序列是否平穩(wěn)，能否達(dá)到建立 VAR模型的建模前提。Sheet GraphM Series: (3D卩 WorkfTe: UNTITLED：!UntitkdView Proc Objfrrt Propertit

4、s Prirt Nam( F疋he Sample Gm 5fi亡也t Graph £Augmented Dicker-Fuller Unit RooiRsl on GDPNull Hypolhesis: GDP has a unit rootExogenous: ConstantLag Lengt!i:3 (Automatic-Based on 3lC, rnaxlag=9i)t-Stati£ticAugmented Dickey Fuller le&l statistic-3.867&530 0056fesl critical values:傅 level

5、-3.6394075% level-2 9511251OT level-2.閃歸MMacKinnon (1996) one-sided pvalues.Auqir&ntsl Dicke 汗 ull 釘 T旳 Equ 抽的Dependent Vanable: DGDP)Melhol Least SquaresDale: W17/17 Time; 10:55Sample (adjusted): 1982 2015Included observations: 34 after adjustmentsVariableCoefficientSid. ErrortStatisticpf)nGDFH

6、)-0,8551710,221114>3,067553ojoooeDtGDPM)0*256310.1935293.2327550J0031D(GDF 國)0 019240017551702B0S4407811D(GDP-3)0.2S49370.1673481.5831450.12+2Ca .540 0502.222S613E417450.0006R-squareriAdjusted R-squared p r0.0529412 545731J rUTU屮呻O.i5S475 Mean dependertvar0 腕3732 S.D dependentvar圖2.1經(jīng)濟(jì)增速(GDP的單位根檢

7、驗(yàn)圖22能源生產(chǎn)增速（nysc）的單位根檢驗(yàn)經(jīng)過檢驗(yàn)，在1%的顯著性水平上，gdp和nysc兩個(gè)時(shí)間序列都是平穩(wěn)的，符合建模的條件，我們建立一個(gè)無約束的VAR模型。3.VAR模型的估計(jì)0 Series: NYSC WorkfJle： UN TITLED:; Un th血或View ProcPrintNameFreeze ISampleGenrObject 1 Properties JAugmenled Dicke Tull er Unit Root Test on MVSChull Hiflpothesis: NYSC has a unit rootExogenous; ConstantLag

8、 Length: 1 (Automatic;-based on £IC,na(lag=9)t-StatisticProE)/Augment層 d Dicfcey-Fuirerte st statist! c-3 9359870.0045Test critical values.1 % level 5% level 10% level-3 526784-2 945542-2.611531MacKinnon 1996)one-sided p-values.AugrnentecJ Dicfcay-FLiIler Test Equation Dependent Variable: D(NYS

9、C) Method: Least SquaresDate; 05/17/17 Time; iui;53Sample (adjusted; 1S90 2Q1Included observations; 36 after adjustmentsVariableCoelTicienlStd. Errort-StatsticProb,hYSCt-1)-0 5309360 134905-39359'870 0004DNYSCC-1)043354901500552 9225850 0062C2.74693S0 35726S3 204SOO0 00301R*squared0.343060Mean d

10、ependent var-0 069444Adjusted R-squared0.303254S.D. dependent var3 510704S,E of regression£93043,11Akaike into criterion5.0673311Sum squared res id2S3.3S51Schwarz criteion5.109791LogliKelihood-83.22096Hannar-Quinncriter5.113689F-statisticS. 616746Durbin-Watsor slat1.990261卩 ro&F-£tati&

11、#163;tic)0.000975Vi«wprocobj«rt1 Print II FreezeEstiimatelFarefajtls''Vector Autoregression EstimatesVe ctor Autor&o ression EstimatesDate: 05/17/17 Time'11:03Sample (adjustedX 1980 2015Indudetllobservations: 3&after adjustments Etarciard errors 泊()&t-siatistics in

12、GDPNYSCGDPt-1)018255440.1S499>150036901.271593 (0.23&99) l.lfiO'SSJGDP 卜 2)-0.5304950.10'&25>-3119096-0 292350 (073760) -172 942NYSCM-01052225 011565> -0 451E601.545356(0.1GS43) (5 11&12NYSC(-2)o.ieeioo(0.1134'9>1.63977-0.357563,0.16234)-2.20263JC6.194518 (1 &

13、0SB7> 4,105392 653291 2.158 27)1 1.326651R-squared0.4925650,5543 酥A也一 R-squared0.4270690496SS9Sum sq. reside1305154267.0333S E equation2.0518692934955F-statMic7.522 S9O9641791Log likelihood-74 26525-87.15117AfcaitaAIC4.4036255119509Schwarz SC4.S2355e5339442Mean dependent9.7330695 016667S.D. tf&am

14、p;perden!2.710S544 137S05Determinant resid covariance (doadj.)30.72290Deterrninant rest'd covariance22 73215Log likelihood-158.4312A tai fee info rm alien criterion9357287Schwa IT criterion9 797154圖3.1模型的估計(jì)結(jié)果回 Van VAR01 Workflle:売龍的模型;Untitled、=II回區(qū)Vi ew |丹0勺0心Etinatioa Free；Ptint Name FreezeEst

15、imate IFo recast i Stats impuLe IReside .LS 1 2 cap lITfEC Wo dal ；GDP = c(l, iMnrC-l) + C(1,2>G-DFC-2)+ CC1,3>KV£C(-1) + C(b4)*lIVSC()4 C&HVSn = CC2. DiGBPC-lO + CC2.2)*GBP(-2)+ CC2.3)*mfSC H) +4)*HYSC(-2)VAE Model - Su.Bstituted Ce£ficitnts.GDI = 0. 3£bb4431£335*DP(-l

16、) - 0. 530434(-2)- *HTSC(-1) +0 leeiOOSOTSlWSCH) + e.l915ie£4?63 tlYSC = O.£?15e7998674*GiFC-15 - 0. £923561651E4*G)PC-2)+ 0. 34S355S60747 狀肛兀(-1) - . 35?567£3£ 74S*JVSC (-£)+ £ 3632310E173圖3.2 模型的表達(dá)式4.模型的檢驗(yàn)4.1 模型的平穩(wěn)性檢驗(yàn)Estimate Fori cast 51回 Var: UNTITLED Workfile；

17、 UNriTLED:Untitled 丫圧wprtx QBMrtj Print Nami Freeze | VAR Stabilrty Condition CheckRoots Off Characteristic Polynomial Endogenous variables: GDr NY3C Exogenous variables: CLag specification: 1 2Date:05/1717 Time. 11:11RootModulus0.5&60G6-0.45-l70Si0 7242200.566066 + 0.451708(0 7242200.269664-0 S

18、2e551i0.6321960.269864 + 0 626551!o.es2igeNo root lies outside the unit 匚ircle. VAR saiisfiesthe siat>iiitcondition.圖4.1.1 AR 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(jì)的模型滿足穩(wěn)定性的條件。Inverse Roots of AR Characteristic Polynomial1_5-l_0-0 6 -0 0 -0.5-1.5-1.5-1.0-0.5O.C 0.51.015根的圖VAR模型估計(jì)，并采用 AR根估計(jì)的方法:如果VAR莫型所圖

19、 4.1.2 AR通過對(duì)GDP增長率和能源生產(chǎn)增長率進(jìn)進(jìn)行了；如果VAR模型所有根模的倒4.1.2可知，沒有根是在單位圓對(duì)VAR模型估計(jì)的結(jié)果進(jìn)行平穩(wěn)性檢驗(yàn)。AR根估計(jì)是基于這樣一種原理的有根模的倒數(shù)都小于 1，即都在單位圓內(nèi)，則該模型是穩(wěn)定的 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 之外的，估計(jì)的 VAR莫型滿足穩(wěn)定性的條件。4.2 Granger 因果檢驗(yàn)r Objft f Priintj| IN am* J F r* j p f Estimat* Iporfa if Imptih問 V円 r: ¥ n FW1 Wo rlrfi g 如1的¥ A R43S

20、ffi!:L J ntirl 戶 cVAR Granuer Oausality/Block Eao口erieity訕mid "TealsDate 05/19/17 TIrrie. 2 0.575amp(a igya 2015Included observations: 36DepEnderrtx/aijable: GDPEndudedCh(-s<iOfPi Ob.NYSC3.03050020.21S&All3 030690£0.21S9口epenc0rvtu3i3bl&- NYSCExcludedChi SCOfPf Ob.GDP1.0902.0! 1

21、20 3071An120 3B71圖 4.2.1Gran ger因果檢驗(yàn)結(jié)果圖Granger因果檢驗(yàn)的原假設(shè)是：HO：變量x不能Granger引起變量y備擇假設(shè)是：H：變量x能Granger引起變量y對(duì)VA( 2)進(jìn)行Gran ger因果檢驗(yàn)在1%勺顯著性水平之下，經(jīng)濟(jì)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(shí)，能源生產(chǎn)增速(NYSC能夠Gran ger經(jīng)濟(jì)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© Vari UNTITLED Worl<filat UNT1 TL£L>j5t制 dVlfitflp

22、rotJobjetl prbrt Mdnie riecze tillni.dlel rorctdst 5Ldl5 liTtpube j. ReUsIlocniVAR Lag Order Selection Criteria Enioenouvariacies: GDP NYSC Exogenous idridibles: DHate.- n5/1717 Tins' H'lfiSample-1973 2015 lndiui(9d i>b£eraticrs 34LagLogLLRrPEAICSCHQ0172.7423NAsgi.eoe'se10.2T8910

23、3&d7103095S1158.355025,坨 394£5.64149'9I597351g.&eeois9.7&921I0I2149 079713.8127*37.ei3<'3*9296S0B"374廠昶"9.45190e*3147 M83IW甜用4北別g汨'O'. 4 DUS 0710 12J1CD.7142344145.4北 d2.9409115£2 650839.51755510423639.e&3131* indicates lag order selected by tti

24、e criterionLR： sequential TUKlifitcl LR lest stall sic (each lest aL 5% level) FPE: Final prediction erroAIC: /ikaiPce information criterian3C： Schwan infornalion criterionHQ: Hannan-Quinn inTomatior critsricn圖5.1 VAR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(yīng)該選擇 VAR (2)進(jìn)行后續(xù)的分析。6.脈沖函數(shù)object

25、 Print' name回 Var： VAR01 Workfile：rVJrtitledI Estimate I Forecast Stats I Impulse I Res.i>ds I 2Vi ewJ Pro cResper » Q Oxiesly 5e 5 & Innvlicns 程 3 Eflasrtsa t£<SDP to GOPHcwkvwMG護(hù) ITZLU圖6.1各因素脈沖響應(yīng)函數(shù)結(jié)果圖從圖6.1可以看出：經(jīng)濟(jì)增長率（GDP和能源生產(chǎn)（NYSC各自對(duì)于自身的沖擊，在前四期是快速下降的 趨勢(shì)，并且出現(xiàn)負(fù)值的情況。但是， GDP曽速的變

26、化基本上在第七期就保持了持平的一個(gè)狀 況；而能源生產(chǎn)（NYSC的變化是在第九期的時(shí)候?qū)崿F(xiàn)持平的狀態(tài)。能源生產(chǎn)增長率（NYSC對(duì)于經(jīng)濟(jì)增長率（GDP的脈沖響應(yīng)分析，當(dāng)給經(jīng)濟(jì)增長一個(gè) 正的沖擊的時(shí)候，在前兩期是呈現(xiàn)一個(gè)下降的趨勢(shì)，主要的原因應(yīng)該是， 經(jīng)濟(jì)增長促進(jìn)能源生產(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(shì)在第五期的時(shí)候達(dá)到最大值， 之后出現(xiàn)了下降的趨勢(shì)， 然后又回升，直到第十期之后保持了平衡。這說明經(jīng)濟(jì)增長對(duì)于能源生產(chǎn)增長的影響是正向的，會(huì)呈現(xiàn)一種上升、下降、平衡的基本狀態(tài)，說明經(jīng)濟(jì)發(fā)展對(duì)能 源生產(chǎn)的促進(jìn)作用并不是無限的，經(jīng)過一定作用之后看，會(huì)出現(xiàn)一種平衡狀態(tài)。經(jīng)濟(jì)增長率（GDP對(duì)于

27、能源生產(chǎn)增長率（NYSC的脈沖響應(yīng)分析，經(jīng)過對(duì)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(dāng)在本期給能源生產(chǎn)增長率（NYSC 個(gè)正沖擊之后，前兩期是增長，然后到第五期是下降趨勢(shì)，然后回升， 在第七期之后基本上持平。7.方差分析畫 Van UrsJTITLED Worfcfile; UNTITLED：'UntitleclView iProcObjert)EstimateForet a ftStatsImpulsePrint Name Freezevanance Dec-omposibonVariance Decomposition of GDP: Perio

28、d S E.GDPN¥SC234567a91011234 & 5739012111 JI JI JI 1 1 2 3 nz23242520272329302.051669100.000001.000000a.62&73299.711540:236+53E比瞪冗96.721431.2705702.7e3eoe92.91947A030533Z,84515339 1101110.369692.85117188 8871311.112872 950827eS 4300I711 5993297241087 637341236265237S77737.4'04'9

29、01259&102 575620S7 4023112.55759237754637 3371112.5126937329637 3730712.&2&932.S7340137.3670712532932.S7S52537.3650912.5?491£.&7357e37.3650012$34畀?.97360137.3&52412.634752 07861387.3646612 635342 87362537 36391212.53S032873639S7.3635812.S36322 07363037.3636612.S：36312.573631

30、37.363G412.S5&SS2.37363237 3635012.536422.07Se33S7.3535612.&?&442.87363337.3635612.530442,37363337.3635612,&3S44237363337 3635612 53&442 07063307 3S35612 635442.37363337.3535612.536442 37363337.3035612.53&4+2 S7363337 3035612.53544圖7.1經(jīng)濟(jì)增長（GDP方差分析結(jié)果回 Van UNTITLED Worlcfile： U

31、NTITLED;:Untitled'|¥iirw| Proc Object j print Na me Freeze Estimate Forcta$t J 5tat5 pnipue ftewdMoomVariance DecompositionVariance Cecomposifion of NV3C:Pefi'od3E.GDPNYSC12.93455615 224264.7175324.02209122.5757677.423243419194G237934376 2065244 203620241765175.3234954 2e&1S426.2479573 75205'64,29087527.1457072.S543074 30702327.0092372 900724 31473027 0676472 93235'94.31&40127 1067572 893