第六章练习题与参考解答第四版.docx

1、第六章练习题与参考解答第四版第六章练习题及参考解答6.1表6.5是中国1985-2016年货物进出口贸易总额（）与国内生产总值（）的数据。表6.5中国进出口贸易总额和国内生产总值单位：亿元年份货物进出口贸国内生产总值年份货物进出口贸国内生产总值易总额（Y）（X）易总额（Y）（X）19852066.719098.9200142183.62110863.119862580.410376.2200251378.15121717.419873084.212174.6200370483.45137422.019883821.815180.4200495539.09161840.219894155.917

2、179.72005116921.77187318.919905560.1218872.92006140974.74219438.519917225.7522005.62007166924.07270232.319929119.6227194.52008179921.47319515.5199311271.0235673.22009150648.06349081.4199420381.948637.52010201722.34413030.3199523499.9461339.92011236401.95489300.6199624133.8671813.62012244160.21540367

3、.4199726967.2479715.02013258168.89595244.4199826849.6885195.52014264241.77643974.0199929896.2390564.42015245502.93689052.1200039273.25100280.12016243386.46740598.7资料来源：中国统计年鉴2017（1）建立货物进出口贸易总额的对数 对国内生产总值的对数 的回归方程；（ 2）检测模型的自相关性；（ 3）采用广义差分法处理模型中的自相关问题。【练习题6.1参考解答】回归结果自相关检验图示法图1、2 与 的散点图以及模型残差图由上面两个图可以

4、发现模型残差存在惯性表现，很可能存在正自相关。DW检验由回归结果可知DW统计量为0.3069，同时，在0.05的显著性水平下，因而模型中存在正相关。BG检验阶数5432AIC-1.275502-1.287655-1.276954-1.338140SIC-0.954873-1.012829-1.047933-1.154923滞后阶数从5阶减小到2阶，AIC及SIC达到最小时，滞后阶数为2阶，此时，已知，同时P值为0.0000，在0.05的显著性水平下拒绝原假设，即存在自相关。表2 BG检验2阶回归结果自相关补救DW反算法求由 ，可知 ，可得广义差分方程：表3 广义差分结果-DW反算法DW检验：由

5、回归结果可知DW统计量为1.6284，同时，在0.05的显著性水平下，即已消除自相关。BG检验：阶数5432AIC-1.260821-1.273263-1.337004-1.369938SIC-0.937017-0.995718-1.105716-1.184908滞后阶数从5阶减小到2阶，AIC及SIC达到最小时，滞后阶数为2阶，此时，已知，同时P值为0.6232，在0.05的显著性水平下不拒绝原假设，即已消除自相关。表4 广义差分BG检验2阶回归结果则可知，最终模型为：残差过原点回归求DependentVariable:EMethod:LeastSquaresDate:02/07/18 Ti

6、me:20:48Sample(adjusted):19862016Includedobservations:31afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.E(-1)0.9027060.1089908.2824420.0000R-squared0.695552Meandependentvar0.004999AdjustedR-squared0.695552S.D.dependentvar0.206153S.E.ofregression0.113749Akaikeinfocriterion-1.477927Sumsqua

7、redresid0.388162Schwarzcriterion-1.431670Loglikelihood23.90787Hannan-Quinncriter.-1.462848Durbin-Watsonstat1.579983表5残差序列过原点回归结果回归结果为：，可知。进而得广义差分方程：lnDependentVariable:LNY-0.902706*LNY(-1)Method:LeastSquaresDate:02/07/18Time:20:51Sample(adjusted):19862016Includedobservations:31afteradjustmentsVariab

8、leCoefficientStd.Errort-StatisticProb.C-0.0057750.215666-0.0267780.9788LNX-0.902706*LNX(-1)0.9398970.1708675.5007560.0000R-squared0.510617Meandependentvar1.175339AdjustedR-squared0.493742S.D.dependentvar0.158003S.E.ofregression0.112422Akaikeinfocriterion-1.470776Sumsquaredresid0.366521Schwarzcriteri

9、on-1.378261Loglikelihood24.79703Hannan-Quinncriter.-1.440619F-statistic30.25831Durbin-Watsonstat1.744560Prob(F-statistic)0.000006表6 广义差分-残差序列过原点回归结果DW检验：由回归结果可知DW统计量为1.744560，同时， ，在0.05的显著性水平下，因而模型已不存在自相关。BG检验：阶数5432AIC-1.248335-1.254886-1.318563-1.356845SIC-0.924532-0.977340-1.087275-1.171814滞后阶数从5

10、阶减小到2阶，AIC及SIC达到最小时，滞后阶数为2阶，此时，已知，同时P值为0.7927，在0.05的显著性水平下不拒绝原假设，即已消除自相关。Breusch-GodfreySerialCorrelationLMTest:F-statistic0.205411Prob.F(2,27)0.8156Obs*R-squared0.464615Prob.Chi-Square(2)0.7927TestEquation:DependentVariable:RESIDMethod:LeastSquaresDate:02/07/18 Time:21:30Sample:19862016Includedobse

11、rvations:31Presamplemissingvaluelaggedresidualssettozero.VariableCoefficientStd.Errort-StatisticProb.C0.0036930.2234790.0165250.9869LNX-0.902706*LNX(-1)-0.0030000.177227-0.0169260.9866RESID(-1)0.1211960.1944720.6232050.5384RESID(-2)-0.0393490.201437-0.1953420.8466R-squared0.014988Meandependentvar4.0

12、2E-16AdjustedR-squared-0.094458S.D.dependentvar0.110532S.E.ofregression0.115635Akaikeinfocriterion-1.356845Sumsquaredresid0.361028Schwarzcriterion-1.171814Loglikelihood25.03110Hannan-Quinncriter.-1.296530F-statistic0.136941Durbin-Watsonstat1.970873Prob(F-statistic)0.937095广义差分BG检验2阶回归结果则可知，最终模型为：德宾两

13、步法求构建模型DependentVariable:LNYMethod:LeastSquaresDate:02/07/18 Time:21:43Sample(adjusted):19862016Includedobservations:31afteradjustmentsVariable Coefficient Std.Error t-Statistic Prob.C -0.068979 0.496455 -0.138943 0.8905LNX1.3740570.4219163.2567030.0030LNX(-1)-1.2756850.361334-3.5304850.0015LNY(-1)0

14、.8952960.1274917.0224420.0000R-squared0.995027Meandependentvar10.65304AdjustedR-squared0.994475S.D.dependentvar1.518884S.E.ofregression0.112903Akaikeinfocriterion-1.404662Sumsquaredresid0.344171Schwarzcriterion-1.219631Loglikelihood25.77226Hannan-Quinncriter.-1.344347F-statistic1800.834Durbin-Watson

15、stat1.685337Prob(F-statistic)0.000000德宾两步法回归结果由此可知， ，进而得广义差分方程：lnDependentVariable:LNY-0.895296*LNY(-1)Method:LeastSquaresDate:02/07/18Time:22:03Sample(adjusted):19862016Includedobservations:31afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.C-0.0219770.214312-0.1025490.9190LNX-0.895296*L

16、NX(-1)0.9504930.1590425.9763580.0000R-squared0.551894Meandependentvar1.253138AdjustedR-squared0.536442S.D.dependentvar0.164971S.E.ofregression0.112320Akaikeinfocriterion-1.472580Sumsquaredresid0.365861Schwarzcriterion-1.380065Loglikelihood24.82500Hannan-Quinncriter.-1.442423F-statistic35.71686Durbin

17、-Watsonstat1.731160Prob(F-statistic)0.000002广义差分-德宾两步法回归结果DW检验：由回归结果可知DW统计量为1.731160，同时，在0.05的显著性水平下，因而模型已不存在自相关。BG检验：阶数5432AIC-1.251149-1.258579-1.322263-1.359935SIC-0.927345-0.981033-1.090975-1.174904滞后阶数从5阶减小到2阶，AIC及SIC达到最小时，滞后阶数为 2阶，此时，已知 ， ，同时P值为0.7773，在0.05的显著性水平下不拒绝原假设，即已消除自相关。Breusch-Godfrey

18、SerialCorrelationLMTest:F-statistic0.223042Prob.F(2,27)0.8015Obs*R-squared0.503846Prob.Chi-Square(2)0.7773TestEquation:DependentVariable:RESIDMethod:LeastSquaresDate:02/07/18 Time:22:16Sample:19862016Includedobservations:31Presamplemissingvaluelaggedresidualssettozero.VariableCoefficientStd.Errort-S

19、tatisticProb.C0.0046100.2220210.0207620.9836LNX-0.895296*LNX(-1)-0.0035380.164928-0.0214500.9830RESID(-1)0.1278020.1945140.6570330.5167RESID(-2)-0.0346800.201586-0.1720380.8647R-squared0.016253Meandependentvar-1.88E-16AdjustedR-squared-0.093052S.D.dependentvar0.110433S.E.ofregression0.115456Akaikein

20、focriterion-1.359935Sumsquaredresid0.359914Schwarzcriterion-1.174904Loglikelihood25.07899Hannan-Quinncriter.-1.299620F-statistic0.148695Durbin-Watsonstat1.972560Prob(F-statistic)0.929624广义差分BG检验2阶回归结果则可知，最终模型为：科克兰奥科特迭代法DependentVariable:LNYMethod:LeastSquaresDate:02/07/18 Time:22:38Sample(adjusted):

21、19862016Includedobservations:31afteradjustmentsConvergenceachievedafter16iterationsVariableCoefficientStd.Errort-StatisticProb.C-0.4817443.749680-0.1284760.8987LNX0.9702560.2861873.3902890.0021AR(1)0.8807660.1284896.8548010.0000R-squared0.994721Meandependentvar10.65304AdjustedR-squared0.994344S.D.de

22、pendentvar1.518884S.E.ofregression0.114233Akaikeinfocriterion-1.409380Sumsquaredresid0.365380Schwarzcriterion-1.270607Loglikelihood24.84538Hannan-Quinncriter.-1.364143F-statistic2637.882Durbin-Watsonstat1.701953Prob(F-statistic)0.000000InvertedARRoots.88科克兰奥科特迭代法回归结果DW检验：由回归结果可知DW统计量为1.701953，同时，在0.

23、05的显著性水平下，因而模型已不存在自相关。BG检验：阶数5432AIC-1.196683-1.227634-1.291215-1.308816SIC-0.826622-0.903830-1.013670-1.077528滞后阶数从5阶减小到2阶，AIC及SIC达到最小时，滞后阶数为2阶，此时，已知，同时P值为0.6472，在0.05的显著性水平下不拒绝原假设，即已消除自相关。Breusch-GodfreySerialCorrelationLMTest:F-statistic0.375414Prob.F(2,26)0.6907Obs*R-squared0.870091Prob.Chi-Squa

24、re(2)0.6472TestEquation:DependentVariable:RESIDMethod:LeastSquaresDate:02/07/18 Time:22:42Sample:19862016Includedobservations:31Presamplemissingvaluelaggedresidualssettozero.VariableCoefficientStd.Errort-StatisticProb.C-2.0865514.831163-0.4318940.6694LNX0.1565470.3660070.4277150.6724AR(1)-0.0877980.

25、182587-0.4808570.6346RESID(-1)0.2100670.2430450.8643130.3953RESID(-2)0.0317620.2362270.1344580.8941R-squared0.028067Meandependentvar2.13E-08AdjustedR-squared-0.121461S.D.dependentvar0.110360S.E.ofregression0.116870Akaikeinfocriterion-1.308816Sumsquaredresid0.355125Schwarzcriterion-1.077528Loglikelihood25.28665Hannan-Quinncriter.-1.233422F-statistic0.187707Durbin-Watsonstat1.921934Prob(F-statistic)0.942677BG检验2阶回归结果最终模型