练习题及参考解答第四版

1、第六章练习题及参考解答表是中国1985-2016年货物进出口贸易总额(Yt)与国内生产总值(Xt)的数据。表中国进岀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)19852001198620021987200319882004198920051990200619912007199220081993200919942010199520111996201219972013199820141999201520002016资料来源：中国统计年鉴2017(1) 建立货物进岀口贸易总额的对数I Yt对国内生产总值的对数I nX

2、t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。【练习题参考解答】回归结果LNY MMhX least Squares Date 03dH8 Time M OB 39m 1W52016 tnduodo&servatws 32VafMtMeCoefBaeotSM Errort-9UtstcProdC LHX-2 7147W11521780316W6-8 56412700273314215675ooooo oooooR-squared AOustedR-SQurcd S E ofreyesston Sum squared resid Log utfthood

3、 F-daftstk： ProtXF-sUfcsic)0 983400 0 982846 0207806 1235519 5903157 1777 192 OOOOOCOMean dtpcndenl var S D dependent war 2“ imo cnuoonSctrwarz aiten on HwunOwrm arttr DurtMn-Waon stacw 55866 1586655 -0 243947O2l35tt0 306907lnYt 二-2.714792 + 1.152178lnXt(0.316996)(0.027331)t 二一 8.564142.15675R?二 0.9

4、834F 二 1777.192 DW 二 0.3069自相关检验 图示法图1、2%1与的散点图以及模型残差图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，同时n二32, k二1 ,在的显著性水平下，血=1-37, du = 1.50,因而模型中存在正相关。BG检验阶数5432AICSIC滞后阶数从5阶减小到2阶,AlC及SIC达到最小时，滞后阶数为2阶，此时点二22.57582,已知X2o.O5 5. 99,同时P值为，在的显著性水平下拒绝原假设，即存在自相关。Breusch-Godfrey Serial Conelaton LM TestF

5、 stattsbc Ob$*Rsquared33 4804722 56454Prob F(22S) Prob cm souar00000 0 0000TestEauatonDependent vanatMt RESIDMethod Least SquaresDate 01/19/18 Tinx 2115Sample 1985 2016Inducted observations 32Presample missing value lagged residuals set to zeroVariableCoeffiaentSM ErrorVSUtisbcProb羔RESKX-1)RESX-2)01

6、62807 -00150991020316-0.13167501863290 01616901888330 2093830873763-0 9338205.403134-0 62M590 28970 35840 00000 5345Rsquared Adjusted R-squared SE o regression Sum squared resid Lg likelihood F$Uti$bc0 7051420673550 0 11M02 0S819M25 4433322 32031Mean dependent var SD dependent var Akai “ info crrten

7、on Schwarz criterion HannacvOuim enter DurtwvWateon $Ut888E，6 0 204428 -1 340208 -1 15W91 -1 27W771938912表2BG检验2阶回归结果自相关补救DW反算法求P由DW = 0.3069,可知6 =l-y=1- 畔 =0.84655,可得广义差分方程:lnYt - 0 846551 nYt - 1 = Pi(1 - 0.84655) + p2(lnXt - 0. 84655lnXt - !)+ utDependem Vanable LNY-0 a4655XNY(-1) Method Least So

8、utres03H9H8 Timt 21:20induced obstnrabons 31 after ad|ustmnftsvaruoHCo1)0 153154 100960S0200827”404 菊01063459 3184170 46500 0000R-equatea gusZ R-sguared SE. of ftgresion Sum squared rtsid Log iikMiood F-stobslc0 74M390 74100601124470 366W424 7W17 8683289 oooooooManeSDYsrAKke nMo atenon Schwarz ateno

9、n Hannan-Oumn enter DurtwvWaUg stH1 7M932 0220W4 1 470333 1 377818 -1 4401761628419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，同时n二31, k = 1,在的显著性水平下,血=1-36, du = 1.50,即已消除自相关。BG检验:阶数5432AICSIC滞后阶数从5阶减小到2阶,AlC及SIC达到最小时，滞后阶数为2阶，此时点二0. 945667,已知X 2o. os 2) = 5.99, nR2 = 0.945667 -Codfrey Serial Correlation LM Te

10、stF-stalistic0 419043Prob FQ7)0 6619Obs*R-squared0933278Prob Chiquare(2)0 6271Test EquationDependent Vanable REST)Method Least SquaresDate: 03n 9/18 Time 21 23Sample 1986 2016lrduded observabons 31Presample missing value lagged residuals set to zeroVariableCoefficientStd Errort-StalisbcProbCLNX-0 84

11、655*LNX(-1) RESIDf-1) RESICK-2)0 012511 0 0069020 176037 -0 0006080 213207011182701946440 2027190058678 -0 0617230 906516 -0 0029980 95360.9512037160 9976R-squared gusted R-squared SE of regression Sum squared resid Log likelihood F-stalisftc ProMF-stahstic)0030106 -0 0776600 1147690 35564425 2639S0

12、 2793620839792Mean dependent var SO dependentvar Akaike info crttenon Schwarz cntecion Hannan-Quinn enter DurtMn-Watson stat6 36E-16 0110557 -1371869 1186839 -13115541 985313表4广义差分BG检验2阶回归结果-0 153154则可知，X = 1- 0.84655 二 一 0.998071最终模型为：lnYt = - 0. 998071 + 1. 009608 lnXt 残差过原点回归求PDependent Variable:

13、 EMethod: Least SquaresDate: 02/07/18 Time: 20:48Sample (adjusted): 1986 2016IncIuded observations: 31 after adjustmentsVariableCoefficient Std. Error t-Statistic Prob.EH)R-squaredAd justed R-squared of regressionSum squared residLog Ii keIi hoodDurbin-Watson statMean dependent var dependent varAkai

14、ke infocr iter ionSchwarz cr iter ionHannan-Qui nncr iter.回归结果为：化=0. 902706et - 1可知 p = 0. 902706c表5残差序列过原点回归结果进而得广义差分方程:|3 1(1 - 0. 902706) +|nYt - 0. 902706 lnYt - 1 =0 2(lnXt - 0. 9027061咲 一 JDependent Variable: C LNX (-1)LNY(-1)Method: Least SquaresDate: 02/07/18 Time: 20:51Sample (adjusted): 19

15、86 2016IncIuded observations: 31 after adjustmentsVariableCoefficient Std. Error t-Statistic Prob.R-squaredMean dependent varAdjusted R-squared of regressionSum squared residLog Ii keIi hoodF-statisticProb (F-statistic) dependent varAkaike infocr iter ionSchwarz cr iter ionHannan-Qui nn cr iter.Durb

16、in-Watsonstat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，同时n = 31, k = 1,在的显著性水平下,九=1.36, du = 1-50,因而模型已不存在自相关。BG检验:阶数5432AICSIC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，此时点二0.464615, 已知xaw 2) = 5.99, nR2 = 0.464615 5. 99,同时P值为，在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-statisticProb. F(2

17、. 27)Prob.Obs*R-squaredChi-Square (2)Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 02/07/18 Time: 21:30Sanple: 1986 2016IncIuded observations: 31Presample missing value lagged residuals set to zero.VariableCoefficient Std.Error t-Statistic Prob.C*LNX (-1)RES I DM)RES ID (-2)R-squ

18、aredMe a n depende nt varAdjusted R-squared dependent varAkaike info of regressioncr iter ionSum squared residSchwarz cr iter ionHannan-QuinnLog Ii keIi hoodcr iter.Durbin-WatsonF-statisticstatProb (F-statistic)广义差分BG检验2阶回归结果则可知，X = 1= - 0 059356最终模型为:lnYt = - 0. 059356 + 0. 939897 lnXt 德宾两步法求P构建模型I

19、nYt = 0 i(1 - p ) + 0 2I 从七 B 2 P I rtXt _ 1 + P I nYt - 1 + utDependent Variable: LNYMethod: Least SquaresDate: 02/07/18 Time: 21:43Sample (adjusted): 1986 2016IncIuded observations: 31 after adjustmentsVariableCoefficient Std.Error t-Statistic Prob.CLNXLNX (-1)LNY (-1)R-squaredMean dependent varAd

20、justed R-squared dependent varAka i ke i nfo of regressioncr iter ionSum squared residSchwarz cr iter ionHannan-Qui nnLog Ii keIi hoodcr iter.Durbin-WatsonF-statisticstatProb (F-statistic)德宾两步法回归结果由此可知，P = 0. 895296,进而得广义差分方程:|nYt - 0 8952961nYt - 1 二 |3 i(1 - 0.895296) + (S2(lnXt - 0. 8952961 nXt -

21、 0 +Dependent Variable: *LNY(-1)Method: Least SquaresDate: 02/07/18 Time: 22:03Sample (adjusted): 1986 2016IncIuded observations: 31 after adjustmentsVariableCoefficient Std.Error t-Statistic Prob.C*LNX (-1)R-squaredMean dependent varAdjusted R-squared dependent varAkaike info of regressioncr iter i

22、onSum squared residSchwarz cr iter ionHannan-0ui nnLog Ii keIi hoodcr iter.Durbin-WatsonF-statisticstatProb (F-statistic)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，同时n = 31, k = 1,在的显著性水平下, 此=1.36, du = 1.50,因而模型已不存在自相关。BG检验:阶数5432AICSIC滞后阶数从5阶减小到2阶,AlC及SIC达到最小时，滞后阶数为2阶，此时点二0. 503846, 已知x 20.05 2) = 5.99, nR2

23、 = 0. 503846 5. 99,同时P值为，在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-statisticObs*R-squaredProb. F(2, 27)Prob.Chi-Square (2)Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 02/07/18 Time: 22:16Sanple: 1986 2016IncIuded observations: 31Presample missing value

24、 lagged residuals set to zeroVariableCoefficient Std. Error t-Statistic Prob.C*LNX (-1)RES I DM)RES ID (-2)Adjusted R-squareddependent varR-squaredMean dependent varAka i ke i nfo of regressionSum squared residLog Ii keIi hoodF-statisticProb (F-statistic)cr iter ionSchwarz cr iter ionHannan-Qui nncr

25、 iter.Durbin-Watsonstat广义差分BG检验2阶回归结果则可知，Bi :- 0. 021977c n 1 - 0. 895296 _ _209896最终模型为：Yt 二- 0. 209896 + 0. 950493Xt 科克兰奥科特迭代法Dependent Variable: LNYMethod: Least SquaresDate: 02/07/18 Time: 22:38Sample (adjusted): 1986 2016IncIuded observations: 31 after adjustmentsConvergence achieved after 16 i

26、terationsVariableCoefficient Std. Error t-Statistic Prob.CLNXARAdjusted R-squareddependent varAka ike info of regressionSum squared residLog Ii keIi hoodF-statisticProb (F-statistic)cr iter ionSchwarz cr iter ionHannan-Qui nncr iter.Durbin-WatsonstatInverted AR Roots88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

27、，同时n = 31, k = 1,在的显著性水平下,此=1.36, du = 1.50,因而模型已不存在自相关。BG检验:阶数5432AICSIC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，此时点二0.870091, 已知x 20.05 2) = 5.99, nR2 = 0. 870091 5. 99,同时P值为，在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-statisticProb. F(2. 26)Prob.0bs*R-squaredChi-Square (2)Test E

28、quation:Dependent Variable: RESIDMethod: Least SquaresDate: 02/07/18 Time: 22:42Sanple: 1986 2016IncIuded observations: 31Presample missing value lagged residuals set to zero.VariableCoefficient Std.Error t-Statistic Prob.CLNXARRES 1 DM)RES ID (-2)R-squaredMean dependent varAdjusted R-squared depend

29、ent varAkaike info of regressioncr iter ionSum squared residSchwarz cr iter ionHannan-Qui nnLog 1i ke1i hoodcr iter.Durbin-WatsonF-statisticstatProb (F-statistic)BG检验2阶回归结果最终模型为:lnYx =- 0.481744 + 0. 970256lnXt表是中国1985-2016年国家财政一般公共预算收入、各项税收、经济活动人口（劳动力）以及国民总收入的数据。表中国财政收入等数据年份一般公共预算收入（亿元）Y各项税收合计（亿元）X

30、2经济活动人口（万人）X3国民总收入（亿元）X4198550112198651546198753060198854630198955707199065323199166091199266782199367468199468135199568855199669765199770800199872087199972791200073992200173, 8842002744922003749112004752902005761202006763152007765312008770462009775102010783882011785792012788942013793002014796902015

31、80091201680694资料来源中国统计年鉴2017(1) 建立国家财政一般公共预算收入与各项税收、经济活动人口及国民总收入的回归方程。(2) 检测模型是否存在自相关性，并修正模型。【练习题参考解答】回归结果Yt 二 12815 73 + 0. 802396X2t - 0. 240367X3t + 0080063X4t (3446. 508) (0. 137414)(0. 057824)(0. 026809)t 二 3一 7184695. 839260- 4. 1568772. 986379R2 二 0. 999309 F 二 13497.65 DW 二 0. 572280自相关检验 图示

32、法图1、2 et- I与的散点图以及模型残差图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，同时n二32, k二3,在的显著性水平下，九=124, du = 1.65,因而模型中存在正相关。BG检验阶数5432AICSIC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，此时点二17. 38280, 已知X 20 05 5.99,同时P值为，在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-statisticProb. F(2. 26)Pro

33、b.Obs*R-squaredChi-Square (2)Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 02/08/18 Time: 01:19Sanple: 1985 2016IncIuded observations: 32Presample missing value lagged residuals set to zero.VariableCoefficient Std.Error t-Statistic Prob.CX2X3X4RESIDEDRES ID (-2)R-squaredMean depe

34、ndent varAdjusted R-squared dependent varAka i ke i nfo of regressioncr iter ionSum squared residSchwarz cr iter ionHannan-Qui nnLog Ii keIi hoodcr iter.Durb in-WatsonF-statisticstatProb (F-statistic)表2BG检验2阶回归结果自相关补救DW反算法求P由DW = 0.306575,可知6 = 1 - 7 = 1 -彎型=0.71386,可得广义差分方程:Yt - 0. 71386Yt - 1 二 -

35、0.71386) + p 2(X2t - 0. 71386X2t - 1)+ 03(X3t - 0. 71386X3J 亠 B4(X4t 一 0. 71386X4t - 1) + utDependent Variable: *Y(-1)Method: Least SquaresDate: 02/08/18 Time: 01:41Sample (adjusted): 1986 2016IncIuded observations: 31 after adjustmentsVariableCoefficient Std. Error t-Statistic Prob.C*X2 (-1)*X3(-1)

36、*X4 (-1)R-squaredMean dependent varAdjusted R-squared dependent varAka i ke i nfo of regressioncr iter ionSum squared residSchwarz cr iter ionHannan-Qui nnLog Ii keIi hoodcr iter.Durbin-WatsonProb(F-statistic)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，同时n二31, k二3,在的显著性水平下,九=1.23, du = 1-65,即已消除自相关。BG检验:阶数5432

37、AICSIC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，此时点二13. 39193, 已知X 20.01(5= 15. 09, nR2 = 13.39193 15. 09,同时P值为，在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-statisticProb. F(5. 22)Prob.0bs*R-squaredChi-Square(5)Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 02/08/1

38、8 Time: 01:47Sanple: 1986 2016IncIuded observations: 31Presample missing value lagged residuals set to zero.VariableCoefficient Std. Error t-Statistic Prob.*X2 (-1)*X3 (-1)*X4 (-1)RES I DM)RES ID (-2)RES ID (-3)RES ID (-4)RES ID (-5)R-squaredMean dependent varAdjusted R-squared dependent varAka i ke

39、 i nfo of regressioncr iter ionSum squared residSchwarz cr iter ionHannanQui nnLog Ii keIi hoodcr iter.Durbin-WatsonF-statisticstatProb (F-statistic)表4广义差分BG检验2阶回归结果则可知，“ =0 和86 = 6771.506955最终模型为：Yt = 6771. 506955 + 0. 867534X2t - 0. 148735X3t + 0. 067410X4t 残差过原点回归求PDependent Variable: EMethod: Le

40、ast SquaresDate: 02/08/18 Time: 03:49Sample (adjusted): 1986 2016IncIuded observations: 31 after adjustmentsVariableCoefficient Std. Error t-Statistic Prob.E(-1)R-squaredMean dependent varAdjusted R-squared dependent varAkaike info of regressioncr iter ionSum squared residSchwarz cr iter ionHannan-Q

41、ui nnLog Ii keIi hoodcr iter.Durbin-Watson stat表5残差序列过原点回归结果回归结果为： = 0. 723560et-1?可知 6 二 0.723560进而得广义差分方程：Yt - 0. 723560Yt -二 (1 - 0. 723560)亠 p2(X2t - 0. 723560X2t - 1)+ B3(X3t - 0. 723560X3t - 1) +4(X4t 一 0 723560X4t - 1) + utDependent Variable: *Y(-1)Method: Least SquaresDate: 02/08/18 Time: 03

42、:54Sample (adjusted): 1986 2016IncIuded observations: 31 after adjustmentsC*X2 (-1)*X3 (-1)*X4 (-1)VariableCoefficient Std. Error t-Statistic Prob.R-squaredAdjusted R-squared of regressionSum squared residLog Ii keIi hoodF-statisticProb (F-statistic)Me a n dependent var dependent varAkaike infocr it

43、er ionSchwarz cr iter ionHannan-Qui nncr iter.Durbin-Watsonstat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，同时n二31, k二3,在的显著性水平下,九=1.23, du = 1-65,因而模型已不存在自相关。BG检验:阶数5432AICSIC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，此时点=13.81143, 已知xbm (5= 15.09, nR?二13.81143 15. 09,同时P值为，在的显著性水平下不拒绝原假设，即已消除自相关。Breusch-Godfrey Se

44、rial Correlation LM Test:F-statisticProb. F(5, 22)Prob.Obs*R-squaredChi-Square (5)Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 02/08/18 Time: 03:58Sanple: 1986 2016IncIuded observations: 31Presample missing value lagged residuals set to zero.VariableCoefficient Std. Error t-Stat

45、istic Prob.C*X2 (-1)*X3(-1)*X4 (-1)RES I DM)RES ID (-2)RES ID (-3)RES ID (-4)RES ID (-5)R-squaredAdjusted R-squaredMean dependent var dependent varAka i ke i nfoof regressioncr iter ionSum squared residSchwarz cr iter ionHannan-Qui nncr iter.statLog Ii keIi hoodDurbin-WatsonF-statisticProb(F-statistic)表7广义差分B