自相關(guān)的檢驗與修正

1、實驗2自相關(guān)的檢驗與修正一、實驗?zāi)康模赫莆兆韵嚓P(guān)模型的檢驗方法與處理方法.。二、實驗內(nèi)容及要求：表1列出了 1985-2007年中國農(nóng)村居民人均純收入與人均消費性支出的統(tǒng)計數(shù)據(jù)。利用OLS法建立中國農(nóng)村居民人均消費性支出與人均純收入的線性模型。檢驗?zāi)Ｐ褪欠翊嬖谧韵嚓P(guān)。如果存在自相關(guān)，試采用適當(dāng)?shù)姆椒右韵?。? 1985-2007年中國農(nóng)村居民人均純收入與人均消費性支出(單位：元)年份全年人均純收入(現(xiàn)價)全年人均消費性支 出(現(xiàn)價)消費價格指數(shù)(1985=100)1985397.6317.421001986423.8357106.11987462.6398.3112.71988544.94

2、76.7132.41989601.5535.4157.91990686.3584.63165.11991708.6619.8168.91992784659.8176.81993921.6769.7201199412211016.8124819951577.71310.36291.419961923.11572.1314.419972090.11617.15322.3199821621590.33319.119992214.31577.42314.320002253.4167031420012366.41741316.520022475.61834315.220032622.241943.332

3、0.220042936.42185335.620053254.932555343200635872829348.1200741403224366.9實驗如下:首先對數(shù)據(jù)進(jìn)行調(diào)整，將全年人均純收入和全年人均消費性支出相應(yīng)調(diào)整為全年實際人 均純收入和全年實際人均消費性支出。LLLJ7XL年位全年人構(gòu)辿收人全年人均消費性支出消費價格指數(shù)全年人均實際純收全年人怕實際消費性支出（即價）（J見價）(lliS5=l(J0)19337.6317.42IDO117.42湖心M357lOtfJ調(diào)皿33(3W71117410.17購螂mgm.TiJ2441136傾.站物au歡,4im坳叫3部所1洌53WMf.l41

4、W1豹1m.6SMEL6Omji穌蛔w時817UW-441M3sn.tf7.72：H458-. 51就如im1121dJi2JSWJ44I0.M舛sI577J13M用知：44?.81蜘mu157*.l31Mm.研500.05蜥昭.1蛹化StU頌.鄒501.75r頰21H15判用319,1677,55W5Biw2：ll.31577.-1*314凈仲4如501刷網(wǎng)3147IW知JfiSW117413眼747.6B制320022475.fiim31SJ7S5.115SLB5顧3IW.3柴心RI攻60收J(rèn)WMM3&.4?18S33S.GBTW齡 14J7*0053Z5l. 932555343948部7

5、4頌200635四2ES348. 1i（m.花眠部顧?un32243SS . 91UBJTB7S.711、用OLS估計法估計參數(shù)者 EViewscile Edit Object View Proc Quick Options Window Help data xyf Group； UNTITLED Worklile: UNTITLED；JntilledView | ProcRobjectPrint |Nar |Fte&ze | Defadt Sort|transppse | &ii：-l7Sinpl+7Tltl仲 | Samp恒 |397. Bo&sXY198539T.60DO317.4200

6、1986399.43 DO33B4BQ01967410.47DO353.420019904-1-1.56D0363.05001999380.94DO330.0 BOO199041&.69D0351.110019914-19 6400266.9600199?44344Q0373.19 叩1993458.51D0382.94001994492.34D041D.ODOO199554A.42DQ449.6BOO199661-1.67D0503.03001997649.50DO501.75001998677.53 DO49B.3BOO1999704 52DD501.8BOO2000717 64D0531

7、.85002001747.58 口口55D.OBOO2002785.41 DO581.85002003B16.94D060B.9DOO20040T74.97DO651.07002005948.96D0744.9DOO2006103D.450812.7DOO2007112B.27DS7B.71D0曹 EViews1File Edit Object Vievu Proc Quirk Options Window Help data xyIs y ex Equation: UNTITLED Workfile: UNTITLED:;Untitled.MwllPfixRobject.Print Inia

8、me |feeze |EWmats Fo此Est|stats|R&sds IDepenaentvariaEie: YMethod: Least SquaresDate:04/24M5 1716:12:32Sample 1985 2007incluaea oDsen/aiicns：23CoeffidentStd. Error t StatisticProb.c56.2187814.548583.3&421Q0.0009X0.6909260.02134231.999730.0000R-squared0.979904M世日 n dependentvar495.3D13Adjusted R-squar

9、ed0.978947s.D. dependentvar158.35733.E of regression22977D8Akaike info crilerion9.189613Sum squared resid110B6.B7Schwarz criterion9.2S9551Log likelihood-103 6828Hannan-Ouinn cliter.9.214645F-slatlsUc10Z3.9B3DurtJin-Waison statD.4D9903Prob(F-statistic)O.OOOODO圖形分析:圖4從圖4中可以看出，中國農(nóng)村居民人均消費性支出與人均純收入存在著顯著的

10、正相關(guān) 關(guān)系。估計回歸方程：從圖3中可以得出，估計回歸方程為：Y=56.21878+0.698928Xt=(3.864210)(31.99973)R2=0.979904 F=1023.983 D.W.=0.4099032自相關(guān)檢驗(1)圖示法圖5從圖5中，可以看出殘差的變化有系統(tǒng)模式，連續(xù)為正或連續(xù)為負(fù)，表示殘差項存在 階正自相關(guān)。(2) DW檢驗從圖3中可以得到D.W.=0.409903，在顯著水平去5%, n=23, k=2, dL=1.26,如=1.44。此時0D.W. Q，表明存在正自相關(guān)。(3) B-G檢驗EVicvdsFile Edit Object View Proc Quick

11、 Options Window Helpdata xyIs y exscatty Ecuation: UNTITLfD W&rkfile； UNmLED:Urtitled|ViLA Frac | Ctajedt| F-ir|N占ni= |FneEEE EstinutellF頃匚ja吐| Slats IIResAsbreuscti-GodfreySerial Correlation LM TestF-statistic17.49487Prcb. F(2,19)O.OODOObsR-squaredU.905S7Prcb. Chi-Squarefi)O.OOD6Test Equation:epoi

12、doit Variable: RESIDMeinod. Least squaresDale: 0424/15 Time: 1245Sample: 199&2007Induded observations: 23Presample missino alue lagged residuals setto zero.suemcientstd. Error t-statlstlcProb.c-1.3190739.70422B-0.1359260.0933X0.0028590.0150440.1900590.8513RESID(-1)1.0691660.220224.S5496&D.QDD1RE.SID

13、(-2)-0.3500610.254050-1.4081250.1752R-squared0.643081M世日n dependentvar2.25E-14Adju atedl R-s q u are d0.59251E3.D. dependent rar22 44S9CS.t. of regression1433009AKaiKe info criterion319371Sum squatrd rsid2901 677Schwarz criterion8 516B4L8Log likelihood-91.67276Hannan-Quinn criter.0.369036F-staiistic

14、11.66324DurDin-lrtatsDnstai2020025Prob(F-tatilic)0.000146圖6從圖6中可得到，nR2=14.90587，臨界概率P=0.0006，因此輔助回歸模型是顯著的，即存在自相關(guān)性。又因為，et1，et2的回歸系數(shù)均顯著地不為03.自相關(guān)的修正使用廣義差分法對自相關(guān)進(jìn)行修正: S EViewsFile Edit Object View Proc Quick Options Window HelpIS CXscatxyIs e e(-1) Equation: UNTITLEC Workfile: UNTITLED:UntitledMie祝 |Rqe|

15、口bjectl |Print|Estimate |Forecast|Stats |Resids|Dependent Variable: EMethod: Least SquaresDate: 04724/15 Time: 13:20sample adjusted): 1986 2007Included obseivations: 22 after adjustmentsCoefficientStd. Error t-StatisticProb.EM)0.8150240 1 419105.74324010000R-squared0.610545Mean dependent var0.758751

16、Adjusted R-squared0.610545S.D. dependent var22.67321S.E. or regression14.14951Akaike info criterion8.131626Sum squared resid4204.383Schwarz criterion8.231219Log likelihood-00.99709Hannan-Quinn criter.0.193309Durbin-Watson stat1.251316對原模型進(jìn)行廣義差分，得到廣義差分方程:Yt-0.815024Yt.1=B1(1-0.815024)+B2(Xt -0.815024

17、Xt_1) +ut對廣義差分方程進(jìn)行回歸:File Edit Object View Proc Quick Options Window Help scatx y Is e e(-1lsy-0.315024(-1 )c 1-0.815 D24*K(-1 Equation! UNTTTLED Workfile: UNTITLEDiiUntitledX| View | ProcQojectPrintName Freeze)Forecast StatsResidsDependentvariable: Y-0.S15024*Y(-1Method: Least SquaresDate: 04/24/15

18、 Time: 13:29Sample (adjusted 1906 2007Included observations: 22 after adjustmentsCoefficientStd. Error t-StatisticProb.L、7.7517137.8135560.99209+03330X-0.815024*X(-1)0.7309860.04955814.750220.0000R-squared0.915014Mean depsndentvar114.0050Adljusted R-squared0.911605S.D. dependent var47.75003S.E. of r

19、egression1419673Aka ike info criterionS .23040 8Sum squared resid4030.942Schwarz criterionS329584Loq liKellhood-88.53449Hannan-auinn enter.B .2537 73F-statistic217.5691 urbin-Watson slat1.324681Prob(F-statistic)0.000000圖8從圖8中可以得出此時的D.W.=1.324681，在取顯著水平為5%, n=23, k=2, dL=1.26, 如=1.44，模型中dLDWdu，此時不能確定

20、是否存在自相關(guān)。在廣義差分法無法完成修正的情況下，現(xiàn)建立對對數(shù)模型:genr lnv=loa(y) genr lnK=log(x is inyc m Equdtion; UNTITLED Wbkfilo; UNnTLED;Untitkd| q | Ev低訕|pqc Dbjeci |Print|NameFreeie | |Estitz |Fcre!ast stabs | ResdsDependent variacie: lnyMeth oct Least SquaresDate:04723i!15 Tme:22:52sample: 1985 2007Included Dhsenjalians:

21、23coeniaentsta. Error t-statisticHroD.c0.2654670.D922072.6765310.0030LNX0.9323220.D1269973.41545O.OODQR-squared0.996119Mesan dependent var7.005657Adjusted R-squared0.995934SLD. dependent var0.705712S.E. cf regression0.044999Akaiks infc criterion-3.281332Sum squared residl0.042524Schwarz criterion-3.

22、102653Los HKeiihood39.73600Hannan-Quinn criter.-3.256559F-staiistic52S9.B29Durbin-Watson stat0.479664ProbfF-statistic；o.oqodoo對雙對數(shù)模型進(jìn)行調(diào)整: EViewsFile Edit Object View Proc Quick Options Window Help genr lnx=log(x)Is Iny c IrwIs Iny c Ins ar由O Equation UNTITLED Workfile: UNTITLED:Untitled =回S3 |為愜曲 |

23、Prod| Object | Pint|NamE|FEEcr | | Estimate | Forecast | Stats | Resi Icorrelogram or Residuals ate: 04J23；15 Hme:23:5DSample: 1937 2037Included observalions: 21Q-statistic probabilities adj u ste dl fo r 2 ARMA te rm (s)AutocorrelationPartial CorrelationACFAC-StatProbi 11i 111 -0.099-0.0990.23431 1

24、1 12 0.1900.1321.15251匚11 113 -0.124-0.0951 56540.2111匚11匚14 -0.163-0.2302.36950.3061 11 15 0.1540.1833.03930.3781匚11 116 -0.182-0.1104.15630.385圖10盛 EViewsFile Edit Object View Proc uick Options Window Help genr lnx=log(x) is iny c inxIs Iny c Inx a arn Equation: UNTTTLD Workffle: UNTTTLE赤U曲ledl| | Byewproc|Objert Print|Name|Freeze EstinatE ForecastJ|5tcts|(Resids|BreuBch-Gocffre Serial CornelatiDn LM TestF-statistic0.526522Prob. F(2,15)0.6D12bs*R-squared1377552Prob. Chi-Square(2)0.5D22TestEquationDependent Va