序列相关性的判定与补救

1、实验名称：序列相关性的判定与补救（实验序号：B14201105 ）5.1实验目的掌握自相关问题出现的来源、后果、检验及修正的原理，以及相关的EViews软件操作方法。5.2实验内容以实验五已克服异方差的中国的消费函数模型（见输出结果图5.4）为例，练习检查和克服模型的自相关的操作方法。由图5.4得到的回归式为：Ln yt=-0.0486+0.9561Ln Xt.（6.1）（-0.05）（68.7） R2=0.997,DW=0.55F=47215.3实验步骤检验模型是否存在自相关（1）观察残差图，如图 6.1，可初步判断残差项存在一定程度的正自相关。（2）用DW检验判断是否存在自相关由EView

2、s输出结果（图5.4 ）知DW=0.55，若给定=0.05，查附表，dL=1.08，du=1.36。因为DW=0.55 1.26,依据判别规则，认为误差项ut存在严重的正自相关。.08 -.06.04.02.00.-.02-.04-.06-.08 -90 91 92 93 94 95 96 97 98 99 00 01 02 03 04图6.1（3）用LM检验判断是否存在自相关（见图6.2）在估计窗口选择 View/Residual Tests/Serial Correalation LM TestEVicws - EqualIon; EQD2 lorfcfile; UBTIILE®

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4、 tut TRssi dual Ttst sLabelAdjusted R-squared S.E. of regression Sum squared res id Log likelihood Durbin-Watson stat0.9970.0 033510.014530.7281C err el o gr am Histogram _-Q-xUti £tie«Squar ed Rez i dualsHarmalily TestS&r ial Corr elation LM T .-AKCX LN TestWhite Ktrozkedastii<y 広e

5、 cross terms)White Heteroskedatici ty Cerons term)0.552466 ProbtF-statisticJTOOOOOO图6.2点击后会自动弹出一个设定滞后期（ Lag Specification ）对话框。输入 1，点击 OK键，得到LM检验结果，见图6.3。Breusch-Godfrey Serial Correlation LM Tost：F-statistic12.34154 Probability0.004278Obs*R- squared7.605234 Probability0.005820Test Equation:Dependen

6、t Variable: R ESI IDMethod: Least SquaresDate: 1IKI2/O7 Time： 23 37Presample missing value lagged residuals set lo zero.VariaLle Coefficiient Std Error 1-Statistiic ProL.C0.061715 114517 7135&30 4631LMX-0.007775.010407-0 747D330 4694RESIEJ(-1)0.8623450.2511623.5130530.0043R-squared0.307016Mean d

7、ependent var-1 76E-15Adjusted R-squareJ0 424852S.D. dependent var0032289S.E. of regression0.024487Akaike info criterion*4.404468Sum squared resid0.007196吕匚hwarz criterion-4.262053Log likelihood36.03351F-statistii；B. 170771Durbin-Waflscni st al0.929937Froti(F-statistic)0.014355图6.3根据p-值判断拒绝原假设，所以BG（

8、LM ）检验结果也说明（6.1）式存在自相关（4）用回归检验法判断自相关 将估计结果(6.1)式得到的残差定义为ut,首先做一阶自回归，得到估计结果见图 6.4。 对该估计式采用LM检验法检验其自相关性，如图6.5。可以判断出仍然存在自相关。 用残差的二阶自回归形式重新建立模型，见图6.6。 再次用LM检验法判断其自相关性，如图6.7。从图6.7可以看出，此时p-值已经达到0.3，落在接受域，即认为误差项不存在自相关。对图6.6的输出结果进行整理，可以得到残差的二阶回归式为Ut =1.3436 Ut 1-0&75 L?； 2 + Vt(6.2)(5.18)(-3.03)R 2=0.71

9、,s.e.=0.02,TR2= 1.1Dependent Variable: UMethod： Least SquaresDate:Time: 23;45Sample Adjusted： 1991 2004Included observaiDns; 14 after adjusimerrtVariableCoefficienitStd. Error t-StatisticProb.LJ(-U0.810596O.240E513.39S7BO0.0048R-suared0 470433Mean dependent var-0.000137Adjusted R'Squared0.470493

10、S.D. dependent var0.033503S.E. of regression0.024379Aka ike info criterion4.521410Sum squared nesiid0.007727Schwarz criteirion4.475771Log likelihood32.64992Diirbin-WatEon etat0.641759图6.4Breusch-Godfrey Serial Correlation LM Test:F-statisticOb s*R-squared10.011156.140424ProbabilityProbability0.00815

11、90.013213Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 10/D2AF Time: 23:45Presampl& missing value lagged residuals set to zero.VariableCoefficientStd Error 店StatisticProb.U(1)RESID (-II-0.4726110.9978060.237849-1.987D210.3153583.16404C0.07020.0002R-squaredAdjusted R-squaredS.

12、E. of regression Sum squared resid Log likelihood0.4366020.3918160.0187360.0D421235.39642hlear dependent 7ar S.D. dapendert var Akaike infb critei'ianSchwarz criterion Durbin-Watsor stat<1.0039930.024025-4.906203-4.6939092.307851图6.5Depend a ni Vanble: UMethod: L申細 Sqw倍Date: W2/O7 Time- 23 46

13、Sample (adjusted): 19922004Included observations. 13 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.0(-1)1.3436080.2592895.1818970.0003U(-2)-0.6175490.209255-3.D363340.0113R-squared0.711709Mean dependent 曲r-0.00042Adjusted R-squared0.695506S.D. dependent var.034047S.E. of regression0.

14、019539Akaike info criterion-4.892131Sum squared resid0.004200Schwarz criterion-4.805216Log likelihood33.79005Durbin-Watson stat2.312116图6.6Breu?ch-Godfrey Serial Correlation LM Test;F-etatisticOLs*R-squared0.9359861.057311ProbabilityProbability0.3561280.303928Test Equatior:Depe nd ent Variable.RESID

15、Method： Least SquaresDate: 1M2/O7 Time: 23:46Presample missing value lagged residuals &et tozero.Ya riableCoefficientStd. Errort-StatisticProb.U(-1)0.2678450.3790310.7051090.4966U(-2)-0.2063300.344103-0.5996190.5621RESID(-1)-0 4425370.457419-0.9674640.3561R-squared0 031332Mean dependent var-0.00

16、1223Adj uste d Rqusred-0 102401S.D. dependent rar0.018664S.E. of regression0.019596Akaike info critericm-4.827759Sum squared resid0 003840Schwarz crherion-4.607386Log likelihood34.38043Dubiri'Watsciri stat2.087198图6.7532克服自相关D即endent Variable: GDLNYMethod; Least SquaresDate: iaU2/07 Time: 23:56S

17、ample (adjusted): 1992 2004Included observations. after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C-0.O35U10.121147*0.2900670.7772GDLNX0.9581090.02302241 620920.0000R-s(luared0 993690Wean depandent var5.002073Adjusted R-squared0.993117S.D. dependent var0.234076S.F. of regression0.01948

18、7Aka ike info criterion-4.897510Sunn squared nesiid0 00A177Sehwarz criterion4.610595Log likelihood33B3332F-st artistic1732.301Durtin-WMson stat2.330506Proh(F statistic)0.000000图6.8Breusch-Godfrey Serial Correlation LM Test:F-staiisticObsTR'Squared0.4790B70.594339ProbabilityProbability0.5045900 4

19、40746T?st Equation;Dependent Variable: RESIDMethod： Least SquaresDate: 1M3/07 Time:00:02Presaniple missing value lagged residuals set tozero.Variable亡 ntStd. Erroi卜 StatisticProb.C.0107190 1250S4-0.0356970.9334GDLIMX0.0020900.0237600.0379040.9317RESID(J)-0.2227860.321070-0 6921610.5046R-squared0.045718Mean dependent4.76E-16Adjusted R-squared-0.14513