1、第六章练习题及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易总额（Y）国内生产总值（X）年份货物进出口贸易总额（Y）国内生产总值（X）19852066.719098.9200142183.62110863.119862580.410376.2200251378.15121717.419873084.212174.6200370483.45137422.019883821.815180.4200495539.09161840.219894155.
2、917179.72005116921.77187318.919905560.1218872.92006140974.74219438.519917225.7522005.62007166924.07270232.319929119.6227194.52008179921.47319515.5199311271.0235673.22009150648.06349081.4199420381.948637.52010201722.34413030.3199523499.9461339.92011236401.95489300.6199624133.8671813.62012244160.21540
3、367.4199719981999200026967.2426849.6829896.2339273.2579715.085195.590564.4100280.12013201420152016258168.89264241.77245502.93243386.46595244.4643974.0689052.1740598.7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Dependent Variable: EMethod: Least SquaresDate: 02/07
6、/18 Time: 20:48Sample (adjusted): 1986 2016Included observations: 31 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.E(-1)0.9027060.1089908.2824420.0000R-squared0.695552Mean dependent var0.004999Adjusted R-squared0.695552S.D. dependent var0.206153S.E. of regression0.113749Akaike info c
7、riterion-1.477927Sum squared resid0.388162Schwarz criterion-1.431670Log likelihood23.90787Hannan-Quinn criter.-1.462848Durbin-Watson stat1.579983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：lnDependent Variable: LNY-0.902706*LNY(-1)Method: Least SquaresDate: 02/07/18 Time: 20:51Sample (adjusted): 1986 2016Incl
8、uded observations: 31 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C-0.0057750.215666-0.0267780.9788LNX-0.902706*LNX(-1)0.9398970.1708675.5007560.0000R-squared0.510617Mean dependent var1.175339Adjusted R-squared0.493742S.D. dependent var0.158003S.E. of regression0.112422Akaike info
9、criterion-1.470776Sum squared resid0.366521Schwarz criterion-1.378261Log likelihood24.79703Hannan-Quinn criter.-1.440619F-statistic30.25831Durbin-Watson stat1.744560Prob(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-1.248335-1.254886-1.3
10、18563-1.356845SIC-0.924532-0.977340-1.087275-1.171814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0.7927，在0.05的显著性水平下不拒绝原假设，即已消除自相关。Breusch-Godfrey Serial Correlation LM Test:F-statistic0.205411Prob. F(2,27)0.8156Obs*R-squared0.464615Prob. Chi-Square(2)0.7927Test Equation:Dependent Variable: RESIDMe
11、thod: Least SquaresDate: 02/07/18 Time: 21:30Sample: 1986 2016Included observations: 31Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb.C0.0036930.2234790.0165250.9869LNX-0.902706*LNX(-1)-0.0030000.177227-0.0169260.9866RESID(-1)0.1211960.1944720.62320
12、50.5384RESID(-2)-0.0393490.201437-0.1953420.8466R-squared0.014988Mean dependent var4.02E-16Adjusted R-squared-0.094458S.D. dependent var0.110532S.E. of regression0.115635Akaike info criterion-1.356845Sum squared resid0.361028Schwarz criterion-1.171814Log likelihood25.03110Hannan-Quinn criter.-1.2965
13、30F-statistic0.136941Durbin-Watson stat1.970873Prob(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：德宾两步法求构建模型 Dependent Variable: LNYMethod: Least SquaresDate: 02/07/18 Time: 21:43Sample (adjusted): 1986 2016Included observations: 31 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C-0.06
14、89790.496455-0.1389430.8905LNX1.3740570.4219163.2567030.0030LNX(-1)-1.2756850.361334-3.5304850.0015LNY(-1)0.8952960.1274917.0224420.0000R-squared0.995027Mean dependent var10.65304Adjusted R-squared0.994475S.D. dependent var1.518884S.E. of regression0.112903Akaike info criterion-1.404662Sum squared r
15、esid0.344171Schwarz criterion-1.219631Log likelihood25.77226Hannan-Quinn criter.-1.344347F-statistic1800.834Durbin-Watson 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：lnDependent Variable: LNY-0.895296*LNY(-1)Method: Least SquaresDate: 02/07/18 Time: 22:03Sample (adjusted): 1986 201
16、6Included observations: 31 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C-0.0219770.214312-0.1025490.9190LNX-0.895296*LNX(-1)0.9504930.1590425.9763580.0000R-squared0.551894Mean dependent var1.253138Adjusted R-squared0.536442S.D. dependent var0.164971S.E. of regression0.112320Akaike
17、info criterion-1.472580Sum squared resid0.365861Schwarz criterion-1.380065Log likelihood24.82500Hannan-Quinn criter.-1.442423F-statistic35.71686Durbin-Watson stat1.731160Prob(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.
18、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 Serial Correlation LM Test:F-statistic0.223042Prob. F(2,27)0.8015Obs*R-squared0.503846Prob. Chi-Square(2)0.7773Test Equation:Dependent Variable: RESIDM
19、ethod: Least SquaresDate: 02/07/18 Time: 22:16Sample: 1986 2016Included observations: 31Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb.C0.0046100.2220210.0207620.9836LNX-0.895296*LNX(-1)-0.0035380.164928-0.0214500.9830RESID(-1)0.1278020.1945140.6570
20、330.5167RESID(-2)-0.0346800.201586-0.1720380.8647R-squared0.016253Mean dependent var-1.88E-16Adjusted R-squared-0.093052S.D. dependent var0.110433S.E. of regression0.115456Akaike info criterion-1.359935Sum squared resid0.359914Schwarz criterion-1.174904Log likelihood25.07899Hannan-Quinn criter.-1.29
21、9620F-statistic0.148695Durbin-Watson stat1.972560Prob(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Dependent Variable: LNYMethod: Least SquaresDate: 02/07/18 Time: 22:38Sample (adjusted): 1986 2016Included observations: 31 after adjustmentsConvergence achieved after 16 iterationsVariableCoe
22、fficientStd. Errort-StatisticProb.C-0.4817443.749680-0.1284760.8987LNX0.9702560.2861873.3902890.0021AR(1)0.8807660.1284896.8548010.0000R-squared0.994721Mean dependent var10.65304Adjusted R-squared0.994344S.D. dependent var1.518884S.E. of regression0.114233Akaike info criterion-1.409380Sum squared re
23、sid0.365380Schwarz criterion-1.270607Log likelihood24.84538Hannan-Quinn criter.-1.364143F-statistic2637.882Durbin-Watson stat1.701953Prob(F-statistic)0.000000Inverted AR Roots.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0.05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
24、-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-Godfrey Serial Correlation LM Test:F-statistic0.375414Prob. F(2,26)0.6907Obs*R-squared0.870091Prob. Chi-Square(2)0.6472Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 02/07/18 Time: 22:42Sample: 1986 2016Included observations: 31Presample missing value lagged residuals set to zero.VariableCoefficientStd.
