实验五 序列相关的检验和修正

1、实验五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GDPCONSCPITAXGDPCXY19783605.61759.146.21519.287802.66678.93806.819794092.62011.547.07537.828694.77552.14273.419804592.92331.250.62571.709073.37943.94605.319815008.82627.951.90629.899650.98437.25063.419825590.02902.952.95700.0210557.19235.15482.319836216.23231.154.00775

2、.5911511.510075.25983.519847362.73742.055.47947.3513273.311565.46746.019859076.74687.460.652040.7914965.711600.87728.6198610508.55302.164.572090.3716274.613037.28211.4198712277.46126.169.302140.3617716.314627.88840.0198815388.67868.182.302390.4718698.215793.69560.3198917311.38812.697.002727.4017846.

3、715034.99085.2199019347.89450.9100.002821.8619347.816525.99450.9199122577.410730.6103.422990.1721830.818939.510375.7199227565.213000.1110.033296.9125052.422056.111815.1199336938.116412.1126.204255.3029269.525897.613004.8199450217.421844.2156.655126.8832057.128784.213944.6199563216.928369.7183.416038

4、.0434467.531175.415467.9199674163.633955.9198.666909.8237331.933853.717092.5199781658.536921.5204.218234.0439987.535955.418080.2199886531.639229.3202.599262.8042712.738140.519363.9199991125.041920.4199.7210682.5845626.440277.620989.6200098749.045854.6200.5512581.5149239.142965.622864.42001108972.449

5、213.2201.9415301.3853962.846385.624370.22002120350.352571.3200.3217636.4560079.051274.926243.72003136398.856834.4202.7320017.3167281.057407.128034.52004160280.463833.5210.6324165.6876095.764622.730306.02005188692.171217.5214.4228778.5488001.274579.633214.02006221170.580120.5217.6534809.72101617.5856

6、24.136811.61、建立回归模型，模型的OLS估计Y = P +P X +pt 01 t t（1）录入数据打开 EViews6，点“File” T New” T “Workfile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:估计回归方程 在命令行输入命令：LS Y C X,回车点八、或者在主菜单中点“Quick”“Estimate Equation”，在 Spe

7、cification 中输入 Y C X,“确定”。得到如下输出:写出估计结果:Y = 2091.28 + 0.4375 X(6.243)(47.059)R 2 =0.9880R 2 = 0.9875F=2214.537D.W.=0.277 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这种模式的残差意味着模型可能存在正的序列相关性。接着连续几期都大于0，做和的关系图:tt 1SCAT E(-1) E2,400 -| TOC o 1-5 h z 2,000 -* *1,600 -*11,200 - 800 -400 -f0-.-400 - 0），

8、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，=1.34, d =1.48，显然00.277，因此模型存在一阶正的自相关。（3）回归检验法拟合模型： = P +8，并运用OLS估计模型：LS E E（-1） tt1t得到如下结果：O Equation: UNTITLED Workfile: XULIEX1ANGGUAN:U.|匝Idbject| Print II Name | Feeni|Estimate I ForecastStatsR巳吕ichDependent Variable: EMethod: Le

9、astSquaresate: 11/07/12 Time: 21:17Sample (adjusted): 1979 2006Included observations: 28 after adjustmentsCoefficientStd. Error t-StatisticProb.0.94S9720.1164608.1404910.0000R-squared0.710391Mean dependent var43.09574Adjusted R-squared0710391S.D. dependent var1031.932S.E. of regression555.3373Akaike

10、 info criterion15.51209Sum squared resid8326787Schwarz criterion15.55967Log likelihood-216.1693Hannan-Quinn criter.15.52663urbin-Watson stat0.576494写出回归结果：e = 0.949tt1(8.148)回归系数的t统计量为8.148,伴随概率P=0.0000va=0.05,表明原模型存在一阶序列相 关。拟合模型：e = P e +P e +，并运用OLS估计模型：LS E E(-1) E(-2) t 1 t12 t2t得到如下结果：Dependent

11、 Variable: EMethod: Least SquaresDate: 11/07/12 Time: 21:24Sample (adjusted): 1930 2006Included observations: 27 after adjustmentsCoefficientStd. Error t-StatisticProb.1.6&86910.15224310.895000.0000E(-2)-0.8643560.155255-55673450.0000R-squared0.364051Mean dependent var86.25222Adjusted R-squared0.8&8

12、613S.D. dependent var1025.517S.E. of regression385.6093Akaike info criterion14.81872Sum squared resid371737 4.Schwarz criterion14.91470Log likelihood-198.0527Hannan-Quinn criter.14.84726urbin-Watson stat2.317512写出回归结果：Ae e=1.659 0.864tt1t2(10.895) (-5.567)回归系数-和七的t统计量分别为10.895、-5.567,相应的伴随概率P=0.0000

13、va=0.05, 表明原模型存在二阶序列相关。拟合模型： = P +P +P +8，并运用OLS估计模型:LS E E(-1) E(-2) t 1 t-12 t-23 t-3tE(-3)，回车，得到如下结果：Dependent Variable: EMethod: Least Squaresate: 11/07/12 Time: 2136Sample (adjusted): 1981 2006Included observations: 26 after adjustmentsCoefficientStd. Errort-StatisticProb.E(-1)1 4953670.2054217

14、.2795340.0000E(-2)-0 4741000.371327-1.2767720.2144-0.2060350.241900-1.1824510.2491R-squared0.867062Mean dependent va126.5562Adjusted R-squared0.855502S.D. dependent var1023787S.E. of regression3S9.1710Akaike info criterion1437408Sum squaredesid3433444.Schwarz criterion15.01925Log likelihood-1903631H

15、annan-Quinn criter.14.91583Durbin-Watson stat2.170417写出回归结果：八一一一一e = 1.495。1 - 0.4742 2 - 0.286。3（7.280） （-1.277）（-1.182）回归系数、的t统计量为7.280，相应的伴随概率P1=0.0000a=0.05，表明、显著不为零，但乃和乙的t统计量分别为-1.277、-1.182,相应的伴随概率P2=0.2144, P3=0.2491，均大于a=0.05，表明原模型不存在三阶序列相关。综上，原模型有二阶序列相关。（4）LM检验首先采用OLS估计模型，在弹出的Equation窗口，点Vi

16、ewResidual TestsrSerial correlation LM Test.，弹出下面的对话框：点“OK”。得到下面的输出:Breusch-Godfrey Serial Correlation LM TestF-statistic55.34401Prob. F(2,25)0.0000Obs*R-squared2365636Prob. Chi-Square(20.0000Test Equation: ependentVariable: RESIDMethod: Least SquaresDate: 11/07/12 Time:21:47Sample: 1973 2006Include

17、d observations: 29Presample missing value lagged residuals set to zero.CoefficientStd. Errort-StatisticProb.c100.2419170.94010.5864150.5629X-0.0051020.005431-0.93072903609RESIDf-1)1 4631020.1793258.1589260.0000RESID (-2)-0.6124870.224943-2.7227930.0116R-squared0 815754Mean dependent var-1.69E-12Adju

18、sted R-squared0 793644S.D. dependent var1039.573S.E. of regression472.2406Akaike info criterion15.20030Sum squared resid5575280.Schwarz criterion15-468&9Log likelihood-217.5643Hannan-Quinn criter.15.33936F-statistic36.39601Durbin-Watson stat1.946335ProbfF-statistic0.000000从上面的输出可知：LM=23.65686, Prob.

19、Chi-Square(2)=0.0000,小于a=0.05，且辅助回 归中RESID(-1)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 ViewResidual TestsSerial correlation LM Tes在弹出的对话 框里将滞后阶数改为3：点“OK”。得到下面的输出:Breusch-Godfrey Serial Correlation LM Test:F-statistic33.03667Prob. F(3,24)0.0000ObsR-squared23.96054Prob. Ch

20、i-Square(3)0.0000Test Equation:Dependent Variable: RESIDMethod: Least Squares ate: 11/07/12 Time: 21:52Sample: 1978 2006Included observations: 29Presample missing value lagged residuals set to zero.CoefficientStd. Error t-StatisticProb.C29.00937179.43970.1616210.3730X-0.0023040.005910-0.3399030.7000

21、RESID(-1)1.3501960.2010136.7168020.0000RESID (-2)-0.2997830.342530-0.37520 S0.3901RESID (-3-0.3063710.254757-1.2025980.2409R-squared0.326225Mean dependent var-1.69E-12Adjusted R-squared0.79726SS.D. dependent var1039.573S.E. of regression468.0815Akaike info criterion15.29075Sum squared resid5253408.S

22、chwarz criterion15.52649Log likelihood-216.7158Hannan-Quinn criter.1536458F-statistic23.52750Durbin-Watson stat1.864232Prob(F-statistic0.000000这时，LM=23.96054,Prob.Chi-Square(2)=0.0000,小于=0.05,但辅助回归中 RESID(-2) 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2阶序列相 关，不具有3阶的序列相关。3、序列相关的修正(1)广义差分法已知模型具有2阶序列相关，

23、在命令行输入命令:LS Y C X AR(1) AR(2)回车得到下面的输出：Dependent Variable: YMethod: Least SquaresDate: 11/07/12 Time: 21:56Sample (adjusted): 1980 2006Included observations: 27 after adjustmentsConvergence achieved after 64 iterationsCoefficientStd. Errort-StatisticProb.C13034S.32636223.0.0494450.9610X0.2795940.064

24、3824.3092590.0003AR1)1.3902020.2130136.5263850.0000AR2)-0.3921790.233399-1.6305830.1064R-squared0.990829Mean dependent var15656.87Adjusted R-squared0.993676S.D. dependent var9324.872S.E. of regression3393329Akaike info criterion14.62779Sum squared resid2648377.Schwarz criterion14.31977Log likelihood-193.4752Hannan-Quinn criter.14.63488F-statistic6536974 urbin-Watson stat1.951415Prob(F-statistic)0.000000Inverted AR Roots1.0039写出修正后的模型：*=130348.8+0.2796X+1.3902AR(1)-0.3922AR(2)(0.049)(4.309)(6.526)(-1.681)3=0.99883=0.9987F=6536.97D.W=1.9514(2)序列相关稳健估计法在主菜单中点“Quick” “Estimate Equat