自相关检验与假定

1、实验报告成绩课程名称计量经济学指导教师实验日期2010年5月20日院（系经济管理学院专业班级营销09-1实验地点机电楼B250学生姓名学号同组人无 实验项目名称 自相关检验与假定一、实验目的和要求通过Eviews软件估计线性回归模型并计算残差,检验误差项是否存在自相关，用广义最小二乘法估计回归参数。二、实验原理如果模型存在自相关，可以通过检验来解决三、主要仪器设备、试剂或材料计算机,EViews软件四、实验方法与步骤准备工作:建立工作文件，并输入数据。-CREATE A 1978 2000 a b c-DATA CONSUM INCOME PRICE-GENR Y=CONSUM/PRICE-G

2、ENR X=INCOME/PRICE1、相关图分析-SCAT X Y2、估计模型。-GENR et=resid3、自相关检验。-图示法? LINE et? SCAT et(-1et-方程结果窗口，有DW统计量，查表得出结论。-LM(BG检验?在方程窗口中点击 View/Residual Test/Series Correlation LM Test4、自相关的修正。-GENR GDY=Y-0.7*Y (- 1 )-GENR GDX=X-0.7*X (- 1 )-LS GDY C GDX 5、再次检验自相关是否存在。五、实验数据记录、处理及结果分析先定义不变价格(1978=1)的人均消费性支出(

3、t Y)和人均可支配收入(tX )。令 /t Y CONSUM PRICE =/t X INCOME PRICE =得关于t Y和t X的散点图，如下图，显然t Y和t X服从线性关系。假定所建模型形式为01t t t 丫 X u BB =+1200-1000 -*A800*600-«*40CT* <2000400800120016002000X估计线性回归模型并计算残差。下面是Eviews的预计结果Depe ndent Variable: 丫Method: Least SquaresDate: 05/20/11 Time: 09:42Sample: 1978 2000In c

4、luded observati ons: 23Variable Coefficie nt Std. Error t-Statistic Prob.C 111.4400 17.05592 6.533804 0.0000 X 0.711829 0.016899 42.12221 0.0000R-squared 0.988303 Mea n depe nden t var 769.4035 Adjusted R-squared 0.987746S.D. depe nde nt var 296.7204S.E. of regressio n 32.84676 Akaike info criterio

5、n 9.904525Sum squared resid 22657.10 Schwarz criterio n10.00326 Log likelihood -111.9020 F-statistic1774.281 Durbi n-Watson stat0.598571 Prob(F-statistic 0.000000用普通最小二乘法求估计的回归方程结果如下?111.440.7118t tY X =+(6.5 (42.120.9883R = s.e=32.8 DW=0.60 T=23回归方程拟合得效果比较好，但是DW值比较低。残差图如下操作结果如下表分别用DW、LM统计量检验误差项tu是否

6、存在自相关Breusch-Godfrey Serial Correlati on LM Test:F-statistic 7.348402 Probability0.00432 6Obs*R-squared 10.03141 Probability0.00663 3Test Equati on:Depe ndent Variable: RESIDMethod: Least SquaresDate: 05/20/11 Time: 09:49Presample miss ing value lagged residuals set to zero.Variable Coeffici Std. Er

7、ror t-Statistic Prob.ETentC 3.880490 13.54398 0.286510 0.7776 X -0.005664 0.013505 -0.419411 0.6796 RESID(-1 0.5922230.231823 2.554630 0.0194 RESID(-20.139653 0.2366900.5900260.5621R-squared0.436148 Mea n depe nde nt var -1.37E-13Adjusted R-squared 0.347119S.D. depe nde nt var 32.09156S.E. of regres

8、sion 25.93032Akaike info criterion 9.505474Sum squared resid 12775.22 Schwarz criterio n 9.702951Log likelihood -105.3129 F-statistic 4.89893Durbi n-Wats on stat51.776908 Prob(F-statistic0.010926已知DW=0.60,若给定a=0.05,查表得DW临界值1.26L d =,1.44U d =。因为DW=0.06<1.26,认为误差项存在严重自相关。LM ( BG)自相关检验辅助回归方程式估计结果是1

9、0.67903.17100.0047t t t te e X v -=+-+ (3.9)( 0.2)( -0.4) 2R =0.43 DW=2.00 LM=2TR =23 X0.43=9.89因为(20.0513.84X =, LM=9.89> 3.84,所以 LM 检验结果也说明误差项存在一阶正相关。用广义最小二乘法估计回归参数。操作结果如下Depe ndent Variable: GDYMethod: Least Squares Date: 05/20/11 Time: 09:52 Sample (adjusted: 1979 2000In eluded observatio ns:

10、 22 after adjustme ntsVariable Coeffieient Std. Error t-StatistieProb.C 45.24890 12.25862 3.6911910.0014 GDX 0.678232 0.033983 19.95799 0.0000 R-squared 0.952190 Mean depe ndent var269.1295Adjusted R-squared 0.949799 S.D. depe ndent var103.4908 S.E. of regression 23.18764 Akaike info eriteri on9.211

11、624Sum squared resid 10753.33 Schwarz criterio n9.310809Log likelihood -99.32786 F-statistic398.3214Durbi n-Watson stat 2.308814 Prob(F-statistic 0.00000首先估计自相关系数？p?10.702DWP令110.700.70t t t t t t GDY Y Y GDX X X -=-=-以t GDY , t GDX , (19792000为样本再次回归,得45.24890.6782t t GDY GDX =+(3.7 (20.0 20.95R =s.e=23.2 DW=2.31,T=22(19792000回归方程拟合优度依然较好，且DW=2.13.查表得1.26L d =, 1.43U d =。因为DW=2,13<