序列相关的检验和修正

1、序列相关的检验及修正例题：中国居民总量消费函数 数据：年份GDPCONSCPITAXGDPCXY19783605.61759.146.21519.287802.6：6678.93806.819794092.62011.547.07537.828694.7 17552.14273.419804592.92331.250.62571.709073.3 17943.94605.319815008.82627.951.90629.899650.9 18437.25063.419825590.02902.952.95700.0210557.1 19235.15482.319836216.23231.15

2、4.00775.5911511.5 110075.25983.519847362.73742.055.47947.3513273.3 111565.46746.019859076.74687.460.652040.7914965.711600.87728.6198610508.55302.164.572090.3716274.6 113037.28211.4198712277.46126.169.302140.3617716.3 114627.88840.0198815388.67868.182.302390.4718698.2 115793.69560.3198917311.38812.69

3、7.002727.4017846.7 115034.99085.2199019347.89450.9100.002821.8619347.8 116525.99450.9199122577.410730.6103.422990.1721830.8 118939.510375.7199227565.213000.1110.033296.9125052.4 122056.111815.1199336938.116412.1126.204255.3029269.5 125897.613004.8199450217.421844.2156.655126.8832057.1 128784.213944.

4、6199563216.928369.7183.416038.0434467.5 131175.415467.9199674163.633955.9198.666909.8237331.9 133853.717092.5199781658.536921.5204.218234.0439987.5 135955.418080.2199886531.639229.3202.599262.8042712.7 138140.519363.9199991125.041920.4199.7210682.5845626.4 140277.620989.6200098749.045854.6200.551258

5、1.5149239.1 142965.622864.42001108972.449213.2201.9415301.3853962.8 146385.624370.22002120350.352571.3200.3217636.4560079.0 151274.926243.72003136398.856834.4202.7320017.3167281.0 157407.128034.52004160280.463833.5210.6324165.6876095.7 164622.730306.02005188692.171217.5214.4228778.5488001.2 174579.6

6、33214.02006221170.580120.5217.6534809.72101617.5 |85624.136811.61、建立回归模型，模型的OLS估计Y oiXtt（1 ）录入数据打开 EViews6，点File”“New”“WorkfileDated reuhr Frequency vWorkfile structure typeIrregular Dated and Panel workfie5 ma/ be made from Unstructured workfiles by later specifying date anchor Cither identifier se

7、ries.Date specflcatkonCancelrjrmes (optionalorkflie 匚reate选择 Dated-regular frequency”，在 Frequency 后选择 “Annual”，在 Start data后输入 1978, 在End data后输入2006，点击“ ok”。在命令行输入：DATA X Y，回车 将数据复制粘贴到 Group中的表格中:(2) 估计回归方程在命令行输入命令：LS Y C X,回车或者在主菜单中点 Quick ”“ Estimate Equation ”，在 Specification 中输入 Y C X，点“确定”。得到如

8、下输出：EQuatiGTi: rSTITLED Vcrkfile: XULIEX1AN&. 五|xVi餉|pfciiz|olzijEd:| |Print阳巾&|尸佗氏引EHim弧|下口址8丈5怙也|収曲也)Dependent Variable- Yh.lethod: Least SquaresDale: 06/08J12 Time: 18:13Sample: 1976 2006included abserYaflons: 29CoefficientStd. Errorb StatisticProto.c2OQ1.2Q2334 9917S.2427870.0000X0.4375270.00929

9、747.056870.0000R-squared1987955Mean dependentvar1485572Adjusted R-squared19875OQs.d. dependent var9472.09ES.E. of regression1058.650Aka ike info criterion1 6 83335Sum squared resid3025994SSchwarz criterion16.92614Log likelihood242.0908Hannan-Guinn enter16 8&33SF-statistic2514.537Durbin-Wat sen stat0

10、.2771 32Prob(F-statistic)o.ooocoo写出估计结果:Y? 2091.28 0.4375X(6.243)(47.059)2 2F=2214.537D.W.=0.277R =0.9880R0.9875 2、序列相关的检验(1)图示检验法作残差序列的时序图：保存残差虚列：GENR E=RESID作图：PLOT E从图上可以看出，模型的最小二乘残差开始连续几期小于0，接着连续几期都大于这种模式的残差意味着模型可能存在正的序列相关性。做和& 1的关系图：SCAT E(-1) E2,400-1,6002,000 _1,600 -1,200800400 -0 -400 -800-

11、1,20002,000-4,000-2,0004,000从上面的散点图可以看出,et和 1之间可以拟合一个线性模型:et = et i t且回归直线的斜率为正（0），表明模型存在正的序列相关性。（2）DW检验由OLS估计的结果可知：D.W.=0.277。查DW分布的临界值表，k=2 ,n=29时，dL=1.34，du =1.48，显然00.277dL，因此模型存在一阶正的自相关。t，并运用 OLS估计模型：LS E E（-1）（3）回归检验法拟合模型：&= et1得到如下结果： Equation: UNTTTLED Wortdile: XUUEXIANGGUAN:U卜回gView |ptoc|

12、 Object | Print riame Freez亡 Estmate Forecast StatsReadsDepen dent Vari able: ELlettiod Least SquaresDate 11/07/12 Time 2117Sample fadjlisted): 1979 2006Included observaticns: 28 after adjustmentsCoefficientStd. E rro rl-StatsticPre b.Ef-1)0.948 &72Q.1154608.1494910,0000R-squiared0.710391Mean depend

13、entvar4309574Adjusted R-squared0.710391S.D. dependent var1031.932S E. of regr&ssior555.1373Aka ike infb criierion15.51209Sum squared resid8326797.Sctiwarz criterion15.55967Log likelihood-216.1693Hannan-Quinn criter.15.52663口 ur bin AV ats on stat0.576494写出回归结果：?0.949 1(8.148)回归系数的t统计量为8.148,伴随概率P=0.

14、0000 =0.05,表明原模型存在一阶序列相 关。拟合模型：et= 1et 12 2 t，并运用OLS估计模型：LS E E(-1) E(-2)得到如下结果：Dependent Variable: EMethod: Least SquaresDate: 1W7/12 Time: 21124Samplie (adjusted: 1980 2006Included observations: 27 after adjiistmentsCoefficientStd Errort-StatisticProbE(d16585910.15224310.995000,0000E(-2)-0.8643560

15、155255-55673450.0000R-squared0854051viean dependentvar85.25222Adjusted R-sqjaredO.056B13S.D. dependent var1025.517G.E. of regression385.609&AJaike info criterion14.31872Sum squared res id3717374.Schwarz： crite ri on14.91470Log likelihood-19&0527Hannan-Quinn errter14.84726Durbin-Watson stat2.317512写出

16、回归结果:?1.659St 10.864 2(10.895)(-5.567)回归系数-1和-的t统计量分别为10.895、-5.567,相应的伴随概率 P=0.0000 =0.05，表明原模型存在二阶序列相关。拟合模型：et= 1%12%23%3 t，并运用OLS估计模型：LS E E(-1) E(-2)E(-3)，回车，得到如下结果:Dependent Variable: EMethod: Least SquaresDate: 11/07/12 Time:21:36Sample (adjusted: 1381 200SIncluded observations: 26 sft&r adjus

17、lmentsCoefficientStd Erort-StatiSticProb.E(-1)1.4353670.20542172795340.0000E(-2)-04741000371327*1 2767720.2144E卜3)*0.2860350.241900-1.1024510.2491R-squared0.867002Mean dependent var126.556 Adjusted R-squared0 855502S D dependentvar1523.787SE of regression389.1710AkaiKfr info crit&rionM074Q8Sum squar

18、ed resid3403444,Schwarz criterion15.01925Log likelihood-19 O.3531Hannan-Ouinn criter.14.91588DurBirvWateM stat2.1704-17写出回归结果:% 1.495%i 0.474%2 0.286%3(7.280)(-1.277)( -1.182)P1=0.0000. F(2,25)Prob ChkSquare(2)0.00000.0000Test EquationDepends nt VariaNe: RESIDMethod: L&astSquaresDate: 11/C7/12 Time:

19、 21:47Sample： 1973 2006Included observations:Presample missing jadum lagged res iduals set to zero.CoefficientStd Errort-S1atisticPrab-.C100.2419170.94010.5864150.5629X-0.005102O.Oa&481-0.9307290.3009RESID(-1)1.4631020.1793258.15S 9260.0000RESIDES)0.6124S7&.524S4S-5 7257930.0116R-squaredi0 3157&4Mea

20、n depends nt var-169E-12Adjusted Ft-squarect0.793544S.D dependentvar1039 573S.E of regression472.2406Akaike inio criterion1620030Sum qiiard resid5575580.Schwarz criterion15.469S9Laglifeelihood-217.5643Hannan-Cuinn crrter.15.33936F-stati tic35,09501Durhin-Watsun statProb(F-staiistic)DOOOOOO从上面的输出可知：

21、LM=23.65686 , Prob.Chi-Square(2)=0.0000,小于=0.05，且辅助回 归中RESID(-I)和RESID(-2)的系数均显著不为 0 (对应t统计量的P值均小于0.05),说明 模型具有2节序列相关。在 Equation 窗口，点 View框里将滞后阶数改为 3:点“OK”得到下面的输出:Residual Tests Serial corre lation LM Test；在弹出的对话E re u 5 chi -Go Sf re y 3 eri al Cgrr&latiQii LM T&stF-slatisticODsR-squared3803B6723.9

22、6054Prob- FC3.24)Prob Chi-Square(3)0.0000D.0000Test Equation:Dependent Variable RESIIDMethod: Least SquaresDate: 11/07/12 Time:21:52Sample: 197S 2006Included obsenations: 29Pres ample missing value lagged rsiduals set to ero.CoefficientStd Errort-StatisticProbC29 00937179.48970.1616210.8730X-0.00230

23、40.005S10-0.3A99030.7Q00RSID-1)-1.3501960.2010186.7166020.0000RE8ID(-2)-0 2997S3034253C -0 8752030.3901RESIDE)”0 3063710.254757-1.2025980.2409R-squaredD.S2&225LI esn depends nt var-1.B9E-12Adj ustod R-squared0.797253S.D dependentvar1039 573S.E. of regression468.0815Aka ike in1o criterion15.29075Sum

24、squared resU525&斗。乱Schwarz criterion15.52649Leg livelihood-216.7158Hannan-Ouinn crii&r.15 36458F-slatistic28527&0Durbin-Watson stat1.B84232PiotHF-statistic)0.000000RESID(-2)2阶序列相这时，LM=23.96054 , Prob.Chi-Square(2)=0.0000，小于 =0.05，但辅助回归中 和RESID(-3)的系数不显著(对应t统计量的P值均大于0.05),说明模型仅存在 关，不具有3阶的序列相关。3、序列相关的

25、修正(1)广义差分法已知模型具有2阶序列相关，在命令行输入命令:LS Y C X ARAR(2)回车得到下面的输出：Dependant VariaWe： YMethod: L&a st SquaresDaU;11W7/12 Time: 21:55Sample (adjusted): 1980 2006Included obsen/atians. 27 aftsr austmenisCan/ergeftce achieved after 64 it&ratinsCoefficientStd 仃。t-StatisticProb,c13D348 826362230.049445D.9610X0.27

26、9594D064ES24.309250D.OOD3AR1.3902020.2130135.5263850.0000AR-0.3921790.233359-1.6805830.1064R-squared0.998829Mean dependentvar15&56,37Adjusted R-squared0.99&676S.D dependentvar9324.072S.E of regression339.3329Akai ke info crite rion1462779Sum squared resid2648377.Schwarz criterion14.31977LoliKelitiood-193.4752Hmnri an-Quin n crikr.倔&488F-statisticS536.974Dur bin-. Vatson siat1.951415Pro b(P-statsticJ0.000000Inverted AR Roots1.00.39写出修正后的模型: =130348.8+0.2796X+1.3902AR(1)-0.3922AR