自相关的检验与修正

1、实验2自相关的检验与修正一、实验目的：掌握自相关模型的检验方法与处理方法.。二、实验内容及要求：表1列出了 1985-2007年中国农村居民人均纯收入与人均消费性支出的统计数据。利用OLS法建立中国农村居民人均消费性支出与人均纯收入的线性模型。检验模型是否存在自相关。如果存在自相关，试采用适当的方法加以消除。表1 1985-2007年中国农村居民人均纯收入与人均消费性支出(单位：元)年份全年人均纯收入(现价)全年人均消费性支 出(现价)消费价格指数(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实验如下:首先对数据进行调整，将全年人均纯收入和全年人均消费性支出相应调整为全年实际人 均纯收入和全年实际人均消费性支出。LLLJ7XL年位全年人构辿收人全年人均消费性支出消费价格指数全年人均实际纯收全年人怕实际消费性支出（即价）（J见价）(lliS5=l(J0)19337.6317.42IDO117.42湖心M357lOtfJ调皿33(3W71117410.17购螂mgm.TiJ2441136倾.站物au欢,4im坳叫3部所1洌53WMf.l41

4、W1豹1m.6SMEL6Omji稣蛔w时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颂.邹501.75r颊21H15判用319,1677,55W5Biw2：ll.31577.-1*314净仲4如501刷网3147IW知JfiSW117413眼747.6B制320022475.fiim31SJ7S5.115SLB5顾3IW.3柴心RI攻60收JWMM3&.4?18S33S.GBTW龄 14J7*0053Z5l. 932555343948部7

5、4颂200635四2ES348. 1i（m.花眠部顾?un32243SS . 91UBJTB7S.711、用OLS估计法估计参数者 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图形分析:图4从图4中可以看出，中国农村居民人均消费性支出与人均纯收入存在着显著的

10、正相关 关系。估计回归方程：从图3中可以得出，估计回归方程为：Y=56.21878+0.698928Xt=(3.864210)(31.99973)R2=0.979904 F=1023.983 D.W.=0.4099032自相关检验(1)图示法图5从图5中，可以看出残差的变化有系统模式，连续为正或连续为负，表示残差项存在 阶正自相关。(2) DW检验从图3中可以得到D.W.=0.409903，在显著水平去5%, n=23, k=2, dL=1.26,如=1.44。此时0D.W. Q，表明存在正自相关。(3) B-G检验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顷匚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图6从图6中可得到，nR2=14.90587，临界概率P=0.0006，因此辅助回归模型是显著的，即存在自相关性。又因为，et1，et2的回归系数均显著地不为03.自相关的修正使用广义差分法对自相关进行修正: 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对原模型进行广义差分，得到广义差分方程:Yt-0.815024Yt.1=B1(1-0.815024)+B2(Xt -0.815024

17、Xt_1) +ut对广义差分方程进行回归: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图8从图8中可以得出此时的D.W.=1.324681，在取显著水平为5%, n=23, k=2, dL=1.26, 如=1.44，模型中dLDWdu，此时不能确定

20、是否存在自相关。在广义差分法无法完成修正的情况下，现建立对对数模型:genr lnv=loa(y) genr lnK=log(x is inyc m Equdtion; UNTITLED Wbkfilo; UNnTLED;Untitkd| q | Ev低讪|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对双对数模型进行调整: 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 |为惬曲 |

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图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