第六章练习题及参考解答(第四版).pdf

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YtXt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）19852066.719098.9200142183.62110863.119862580.410376.2200251378.15121717.419873084.212174.6200370483.45137422.019883821.815180.4200495539.09161840.219894155.917179.72005116921.77187318.919905560.1218872.92006140974.74219438.519917225.7522005.62007166924.07270232.319929119.6227194.52008179921.47319515.5199311271.0235673.22009150648.06349081.4199420381.948637.52010201722.34413030.3199523499.9461339.92011236401.95489300.6199624133.8671813.62012244160.21540367.4199719981999200026967.2426849.6829896.2339273.2579715.085195.590564.4100280.12013201420152016258168.89264241.77245502.93243386.46595244.4643974.0689052.1740598.7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；lnlnX（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。【练习题练习题 6.1 参考解答参考解答】回归结果lnYt=2.714792+1.152178 (0.316996)(0.027331)=8.5641 42.15675 2=0.9834 =1777.192 =0.3069自相关检验图示法 图 1、2 与 的散点图以及模型残差图 1e由上面两个图可以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，n=32，=1，因而模型中存在正相关。d=1.37，d=1.50BG 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，n2=22.5758220.05（2）=5.99n2=22.56454 5.99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：DW=0.3069=1-DW2=1-0.30692=0.84655lnYt 0.84655 1=1(1 0.84655)+2(0.84655Xt-1)+表3 广义差分结果-DW反算法DW检验：由回归结果可知DW统计量为1.6284，同时，在0.05的显著性水平n=31，=1下，即已消除自相关。d=1.36，d=1.50BG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，n2=0.94566720.05（2）=5.99n2=0.945667 5.99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，1=0.1531541-0.84655=-0.998071最终模型为：Yt=-0.998071+1.009608残差过原点回归求Dependent Variable:EMethod:Least SquaresDate:02/07/18 Time:20:48Sample(adjusted):1986 2016Included observations:31 after adjustmentsVariableCoefficientStd.Errort-StatisticProb.E(-1)0.9027060.1089908.2824420.0000R-squared0.695552 Mean dependent var0.004999Adjusted R-squared0.695552 S.D.dependent var0.206153S.E.of regression0.113749 Akaike info criterion-1.477927Sum squared resid0.388162 Schwarz criterion-1.431670Log likelihood23.90787 Hannan-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。e=0.902706 1=0.902706进而得广义差分方程：lnYt 0.902706 1=1(1 0.902706)+2(0.902706Xt-1)+Dependent Variable:LNY-0.902706*LNY(-1)Method:Least SquaresDate:02/07/18 Time:20:51Sample(adjusted):1986 2016Included observations:31 after adjustmentsVariableCoefficientStd.Errort-StatisticProb.C-0.0057750.215666-0.0267780.9788LNX-0.902706*LNX(-1)0.9398970.1708675.5007560.0000R-squared0.510617 Mean dependent var1.175339Adjusted R-squared0.493742 S.D.dependent var0.158003S.E.of regression0.112422 Akaike info criterion-1.470776Sum squared resid0.366521 Schwarz criterion-1.378261Log likelihood24.79703 Hannan-Quinn criter.-1.440619F-statistic30.25831 Durbin-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n=31，=1平下，因而模型已不存在自相关。d=1.36，d=1.50BG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，n2=0.46461520.05（2）=5.99n2=0.464615 5.99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-statistic0.205411 Prob.F(2,27)0.8156Obs*R-squared0.464615 Prob.Chi-Square(2)0.7927Test Equation:Dependent Variable:RESIDMethod: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)0.1211960.1944720.6232050.5384RESID(-2)-0.0393490.201437-0.1953420.8466R-squared0.014988 Mean dependent var4.02E-16Adjusted R-squared-0.094458 S.D.dependent var0.110532S.E.of regression0.115635 Akaike info criterion-1.356845Sum squared resid0.361028 Schwarz criterion-1.171814Log likelihood25.03110 Hannan-Quinn criter.-1.296530F-statistic0.136941 Durbin-Watson stat1.970873Prob(F-statistic)0.937095 广义差分BG检验2阶回归结果则可知，1=0.0057751-0.902706=-0.059356最终模型为：lnYt=-0.059356+0.939897德宾两步法求构建模型 Yt=1(1 )+2 2 1+1+Dependent Variable:LNYMethod:Least SquaresDate:02/07/18 Time:21:43Sample(adjusted):1986 2016Included observations:31 after adjustmentsVariableCoefficientStd.Errort-StatisticProb.C-0.0689790.496455-0.1389430.8905LNX1.3740570.4219163.2567030.0030LNX(-1)-1.2756850.361334-3.5304850.0015LNY(-1)0.8952960.1274917.0224420.0000R-squared0.995027 Mean dependent var10.65304Adjusted R-squared0.994475 S.D.dependent var1.518884S.E.of regression0.112903 Akaike info criterion-1.404662Sum squared resid0.344171 Schwarz criterion-1.219631Log likelihood25.77226 Hannan-Quinn criter.-1.344347F-statistic1800.834 Durbin-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：ln=0.895296Yt 0.895296 1=1(1 0.895296)+2(0.895296Xt-1)+Dependent Variable:LNY-0.895296*LNY(-1)Method:Least SquaresDate:02/07/18 Time:22:03Sample(adjusted):1986 2016Included observations:31 after adjustmentsVariableCoefficientStd.Errort-StatisticProb.C-0.0219770.214312-0.1025490.9190LNX-0.895296*LNX(-1)0.9504930.1590425.9763580.0000R-squared0.551894 Mean dependent var1.253138Adjusted R-squared0.536442 S.D.dependent var0.164971S.E.of regression0.112320 Akaike info criterion-1.472580Sum squared resid0.365861 Schwarz criterion-1.380065Log likelihood24.82500 Hannan-Quinn criter.-1.442423F-statistic35.71686 Durbin-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n=31，=1平下，因而模型已不存在自相关。d=1.36，d=1.50BG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，n2=0.50384620.05（2）=5.99n2=0.503846 5.99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-statistic0.223042 Prob.F(2,27)0.8015Obs*R-squared0.503846 Prob.Chi-Square(2)0.7773Test Equation:Dependent Variable:RESIDMethod: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)0.1278020.1945140.6570330.5167RESID(-2)-0.0346800.201586-0.1720380.8647R-squared0.016253 Mean dependent var-1.88E-16Adjusted R-squared-0.093052 S.D.dependent var0.110433S.E.of regression0.115456 Akaike info criterion-1.359935Sum squared resid0.359914 Schwarz criterion-1.174904Log likelihood25.07899 Hannan-Quinn criter.-1.299620F-statistic0.148695 Durbin-Watson stat1.972560Prob(F-statistic)0.929624 广义差分BG检验2阶回归结果则可知，1=0.0219771-0.895296=-0.209896最终模型为：Yt=0.209896+0.950493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 iterationsVariableCoefficientStd.Errort-StatisticProb.C-0.4817443.749680-0.1284760.8987LNX0.9702560.2861873.3902890.0021AR(1)0.8807660.1284896.8548010.0000R-squared0.994721 Mean dependent var10.65304Adjusted R-squared0.994344 S.D.dependent var1.518884S.E.of regression0.114233 Akaike info criterion-1.409380Sum squared resid0.365380 Schwarz criterion-1.270607Log likelihood24.84538 Hannan-Quinn criter.-1.364143F-statistic2637.882 Durbin-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n=31，=1平下，因而模型已不存在自相关。d=1.36，d=1.50BG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，n2=0.87009120.05（2）=5.99n2=0.870091 5.99在0.05的显著性水平下拒绝原假设，即存在自相关。Breusch-Godfrey Serial Correlation LM Test:F-statistic15.45963 Prob.F(2,26)0.0000Obs*R-squared17.38280 Prob.Chi-Square(2)0.0002Test Equation:Dependent Variable:RESIDMethod:Least SquaresDate:02/08/18 Time:01:19Sample:1985 2016Included observations:32Presample missing value lagged residuals set to zero.VariableCoefficientStd.Errort-StatisticProb.C-909.86962473.584-0.3678350.7160X20.1291290.0992501.3010510.2047X30.0179380.0416710.4304720.6704X4-0.0231710.019330-1.1987280.2414RESID(-1)0.6647000.1944813.4178130.0021RESID(-2)0.2841830.2679281.0606690.2986R-squared0.543213 Mean dependent var-4.46E-12Adjusted R-squared0.455369 S.D.dependent var1327.778S.E.of regression979.8889 Akaike info criterion16.78012Sum squared resid24964739 Schwarz criterion17.05494Log likelihood-262.4819 Hannan-Quinn criter.16.87121F-statistic6.183852 Durbin-Watson stat1.984539Prob(F-statistic)0.000667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：DW=0.306575=1-DW2=1-0.5722802=0.71386Yt 0.71386 1=1(1 0.71386)+2(2 0.71386X2t-1)+3(3 0.71386X3t-1)+4(4 0.71386X4t-1)+Dependent Variable:Y-0.71386*Y(-1)Method:Least SquaresDate:02/08/18 Time:01:41Sample(adjusted):1986 2016Included observations:31 after adjustmentsVariableCoefficientStd.Errort-StatisticProb.C1937.5992008.7540.9645770.3433X2-0.71386*X2(-1)0.8675340.1399266.1999450.0000X3-0.71386*X3(-1)-0.1487350.102036-1.4576680.1565X4-0.71386*X4(-1)0.0674100.0264442.5492040.0168R-squared0.997291 Mean dependent var15685.47Adjusted R-squared0.996990 S.D.dependent var17950.24S.E.of regression984.8333 Akaike info criterion16.74274Sum squared resid26187209 Schwarz criterion16.92777Log likelihood-255.5124 Hannan-Quinn criter.16.80305F-statistic3313.118 Durbin-Watson stat1.897337Prob(F-statistic)0.000000表3 广义差分结果-DW反算法DW检验：由回归结果可知DW统计量为1.897337，同时，在0.05的显著性水n=31，=3平下，即已消除自相关。d=1.23，d=1.65BG检验：阶数5432AIC16.4996916.6846516.7902816.78215SIC16.9160117.0547117.1140917.05969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5阶，此时，已知，同时P值为n2=13.3919320.01（5）=15.09n2=13.39193 15.090.0200，在0.01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-statistic3.346450 Prob.F(5,22)0.0213Obs*R-squared13.39193 Prob.Chi-Square(5)0.0200Test Equation:Dependent Variable:RESIDMethod:Least SquaresDate:02/08/18 Time:01:47Sample:1986 2016Included observations:31Presample missing value lagged residuals set to zero.VariableCoefficientStd.Errort-StatisticProb.C-501.36691740.841-0.2880030.7760X2-0.71386*X2(-1)-0.0182870.168376-0.1086100.9145X3-0.71386*X3(-1)0.0203630.0888370.2292230.8208X4-0.71386*X4(-1)0.0049530.0303320.1633090.8718RESID(-1)0.0488990.1934300.2527990.8028RESID(-2)0.3860850.2998871.2874340.2113RESID(-3)0.6204360.3089392.0082810.0570RESID(-4)0.4576780.3575401.2800750.2139RESID(-5)-0.9277830.371591-2.4967880.0205R-squared0.431998 Mean dependent var9.09E-13Adjusted R-squared0.225452 S.D.dependent var934.2949S.E.of regression822.2583 Akaike info criterion16.49969Sum squared resid14874391 Schwarz criterion16.91601Log likelihood-246.7451 Hannan-Quinn criter.16.63540F-statistic2.091531 Durbin-Watson stat1.811014Prob(F-statistic)0.081653表4 广义差分BG检验2阶回归结果则可知，1=1937.5991-0.71386=6771.506955最终模型为：Yt=6771.506955+0.8675342-0.1487353+0.0674104残差过原点回归求Dependent Variable:EMethod:Least SquaresDate:02/08/18 Time:03:49Sample(adjusted):1986 2016Included observations:31 after adjustmentsVariableCoefficientStd.Errort-StatisticProb.E(-1)0.7235600.1362135.3119770.0000R-squared0.484287 Mean dependent var36.56852Adjusted R-squared0.484287 S.D.dependent var1333.245S.E.of regression957.4459 Akaike info criterion16.59814Sum squared resid27501077 Schwarz criterion16.64440Log likelihood-256.2712 Hannan-Quinn criter.16.61322Durbin-Watson stat2.039143表5 残差序列过原点回归结果回归结果为：，可知。e=0.723560 1=0.723560进而得广义差分方程：Yt 0.723560 1=1(1 0.723560)+2(2 0.723560X2t-1)+3(3 0.723560X3t-1)+4(4 0.723560X4t-1)+Dependent Variable:Y-0.72356*Y(-1)Method:Least SquaresDate:02/08/18 Time:03:54Sample(adjusted):1986 2016Included observations:31 after adjustmentsVariableCoefficientStd.Errort-StatisticProb.C1723.3861976.3850.8719890.3909X2-0.72356*X2(-1)0.8686460.1400966.2003830.0000X3-0.72356*X3(-1)-0.1411150.103515-1.3632380.1841X4-0.72356*X4(-1)0.0671450.0264502.5385890.0172R-squared0.997166 Mean dependent var15326.08Adjusted R-squared0.996851 S.D.dependent var17509.19S.E.of regression982.5331 Akaike info criterion16.73806Sum squared resid26065024 Schwarz criterion16.92309Log likelihood-255.4399 Hannan-Quinn criter.16.79837F-statistic3166.688 Durbin-Watson stat1.913774Prob(F-statistic)0.000000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1.913774，同时，在0.05的显著性水n=31，=3平下，因而模型已不存在自相关。d=1.23，d=1.65BG检验：阶数5432AIC16.4709016.6673916.7836216.77818SIC16.8872217.0374517.1074217.05573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5阶，此时，已知，同时P值为n2=13.8114320.01（5）=15.09n2=13.81143 15.090.0169，在0.01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-statistic3.535507 Prob.F(5,22)0.0170Obs*R-squared13.81143 Prob.Chi-Square(5)0.0169Test Equation:Dependent Variable:RESIDMethod:Least SquaresDate:02/08/18 Time:03:58Sample:1986 2016Included observations:31Presample missing value lagged residuals set to zero.VariableCoefficientStd.Errort-StatisticProb.C-437.78351689.050-0.2591890.7979X2-0.72356*X2(-1)-0.0237400.165877-0.1431190.8875X3-0.72356*X3(-1)0.0173070.0888430.1948010.8473X4-0.72356*X4(-1)0.0061210.0298430.2050940.8394RESID(-1)0.0397620.1919180.2071830.8378RESID(-2)0.3926250.2987041.3144250.2022RESID(-3)0.6440810.3066292.1005230.0474RESID(-4)0.4676190.3563291.3123230.2029RESID(-5)-0.9491660.370553-2.5614870.0178R-squared0.445530 Mean dependent var-2.09E-12Adjusted R-squared0.243905 S.D.dependent var932.1127S.E.of regression810.5069 Akaike info criterion16.47090Sum squared resid14452273 Schwarz criterion16.88722Log likelihood-246.2989 Hannan-Quinn criter.16.60661F-statistic2.209692 Durbin-Watson stat1.815636Prob(F-statistic)0.067454表7 广义差分BG检验2阶回归结果则可知，1=1723.3861-0.72356=6234.21357最终模型为：Yt=6234.21357+0.8686462-0.1411153+0.0671454德宾两步法求构建模型：Yt=1(1 )+22 22 1+33 33 1+44 44 1+1+Dependent Variable:YMethod:Least SquaresDate:02/08/18 Time:04:07Sample(adjusted):1986 2016Included observations:31 after adjustmentsVariableCoefficientStd.Errort-StatisticProb.C2223.9702640.6990.8421900.4084X20.9416370.1916654.9129220.0001X2(-1)-0.4851470.367381-1.3205570.1996X3-0.0096900.096118-0.1008180.9206X3(-1)-0.0344630.094140-0.3660800.7177X40.0019980.0433490.0460890.9636X4(-1)0.0087380.0462570.1889030.8518Y(-1)0.6013370.1850523.2495590.0035R-squared0.999831 Mean dependent var42134.25Adjusted R-squared0.999779 S.D.dependent var50837.09S.E.of regression755.6851 Akaike info criterion16.31076Sum squared resid13134378 Schwarz criterion16.68082Log likelihood-244.8168 Hannan-Quinn criter.16.43139F-statistic19392.30 Durbin-Watson stat2.375383Prob(F-statistic)0.000000表8 德宾两步法回归结果由此可知，进而得广义差分方程：=0.601337Yt 0.601337 1=1(1 0.601337)+2(2 0.601337X2t-1)+3(3 0.601337X3t-1)+4(4 0.601337X4t-1)+Dependent Variable:Y-0.601337*Y(-1)Method:Least SquaresDate:02/08/18 Time:04:13Sample(adjusted):1986 2016Included observations:31 after adjustmentsVariableCoefficientStd.Errort-StatisticProb.C4411.5862291.0691.9255580.0648X2-0.601337*X2(-1)0.8471220.1375476.1587840.0000X3-0.601337*X3(-1)-0.2115220.086609-2.4422740.0214X4-0.601337*X4(-1)0.0718350.0262712.7343580.0109R-sq