第五章异方差性.docx

1、第五章异方差性5.3为了研究中国出口商品总额 EXPORT对国内生产总值 GDP的影响，搜集了 19902015年相关的指标数据，如表 5.3所示。表3中国出口商品总额与国内生产总值 (单位：亿元)时间出口商品总额EXPORT国内生产总值GDP时间出口商品总额EXPORT国内生产总值GDP19913827.122005.6200449103.3161840.219924676.327194.5200562648.1187318.919935284.835673.2200677597.2219438.5199410421.848637.5200793627.1270232.3199512451.

2、861339.92008100394.9319515.5199612576.471813.6200982029.7349081.4199715160.779715.02010107022.8413030.3199815223.685195.52011123240.6489300.6199916159.890564.42012129359.3540367.4200020634.4100280.12013137131.4595244.4200122024.4110863.12014143883.7643974.0200226947.9121717.42015141166.8685505.82003

3、36287.9137422.0资料来源：国家统计局网站(1)根据以上数据，建立适当线性回归模型。(2)试分别用White检验法与ARCH检验法检验模型是否存在异方差?(3)如果存在异方差，用适当方法加以修正。解：（1）Dependent Variable: YMethod: Least SquaresDate: 04/18/20 Time: 15:38Sample: 1991 2015Included observations: 25VariableCoefficientStd. Error t-StatisticProb.C-673.086315354.24 -0.0438370.9654X

4、4.0611310.201677 20.136840.0000R-squared0.946323Mean dependent var234690.8Adjusted R-squared0.943990S.D. dependent var210356.7S.E. of regression49784.06Akaike info criterion24.54540Sum squared resid5.70E+10Schwarz criterion24.64291Log likelihood-304.8174Hannan-Quinn criter.24.57244F-statistic405.492

5、4Durbin-Watson stat0.366228Prob(F-statistic)0.000000模型回归的结果：AY 673.0863 4.0611Xit ( 0.0438 )(20.1368)R2 0.9463, n 25(2) white:该模型存在异方差Heteroskedasticity Test: WhiteF-statistic4.493068Prob. F(2,22)0.0231Obs*R-squared7.250127Prob. Chi-Square(2)0.0266Scaled explained SS8.361541Prob. Chi-Square(2)0.0153

6、Test Equation:Dependent Variable: RESIDEMethod: Least SquaresDate: 04/18/20 Time: 17:45Sample: 1991 2015Included observations: 25VariableCoefficientStd. Error t-StatisticProb.C-1.00E+091.43E+09 -0.7003780.4910XA2-0.4554200.420966 -1.0818470.2910X102226.260664.19 1.6851170.1061R-squared0.290005Mean d

7、ependent var2.28E+09Adjusted R-squared0.225460S.D. dependent var3.84E+09S.E. of regression3.38E+09Akaike info criterion46.83295Sum squared resid2.51E+20Schwarz criterion46.97922Log likelihood-582.4119Hannan-Quinn criter.46.87352F-statistic4.493068Durbin-Watson stat0.749886Prob(F-statistic)0.023110AR

8、CH检验：该模型存在异方差Heteroskedasticity Test: ARCHF-statistic18.70391Prob. F(1,22)0.0003Obs*R-squared11.02827Prob. Chi-Square(1)0.0009Test Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 04/18/20 Time: 19:55Sample (adjusted): 1992 2015Included observations: 24 after adjustmentsVariableCoeffic

9、ientStd. Error t-StatisticProb.C8.66E+086.92E+08 1.2516840.2238RESIDA2(-1)0.8171460.188944 4.3248020.0003R-squared0.459511Mean dependent var2.37E+09Adjusted R-squared0.434944S.D. dependent var3.90E+09S.E. of regression2.93E+09Akaike info criterion46.51293Sum squared resid1.89E+20Schwarz criterion46.

10、61110Log likelihood-556.1552Hannan-Quinn criter.46.53898F-statistic18.70391Durbin-Watson stat0.888067Prob(F-statistic)0.000273(3)修正：加权最小二乘法修正却 WF Woricflil-ri U TLECi id tl ecJi T tl t-|p-r f T 护i i-i h 1 5rlucilifl -MII TGR 1 Z7Q I S w= T ,皿”=e Ba-oa 山口 fE=-UH a p-oe= -口曰 3.2 1 且-口9 I B之与尸-口口 ti .3

11、-Z2E-DO 出q,峙尸C旦( 4.3-1 E-O30 3IE 09 N.HMU O-QI 立o右匚 - nO4TDE-W Z.&15=- DC1 hi-tiE - IIIJ i. um r ci Q sjF -iii i旦日二-口Dependent Variable: YMethod: Least SquaresDate: 04/18/20 Time: 20:46Sample: 1991 2015Included observations: 25Weighting series: W2Weight type: Inverse variance (average scaling)Variab

12、leCoefficientStd. Error t-StatisticProb.C10781.172188.706 4.9258210.0001X3.9316060.192004 20.476670.0000Weighted StatisticsR-squared0.947998Mean dependent var51703.40Adjusted R-squared0.945737S.D. dependent var11816.72S.E. of regression8420.515Akaike info criterion20.99135Sum squared resid1.63E+09Sc

13、hwarz criterion21.08886Log likelihood-260.3919Hannan-Quinn criter.21.01839F-statistic419.2938Durbin-Watson stat0.539863Prob(F-statistic)0.000000Weighted mean dep.39406.30Unweighted StatisticsR-squared0.944994Mean dependent var234690.8Adjusted R-squared0.942602S.D. dependent var210356.7S.E. of regres

14、sion50396.82Sum squared resid5.84E+10修正后进行white检验:Heteroskedasticity Test: WhiteF-statistic0.261901Prob. F(2,22)0.7720Obs*R-squared0.581387Prob. Chi-Square(2)0.7477Scaled explained SS0.211737Prob. Chi-Square(2)0.8995Test Equation:Dependent Variable: WGT_RESIDA2Method: Least SquaresDate: 04/18/20 Tim

15、e: 20:41Sample: 1991 2015Included observations: 25Collinear test regressors dropped from specificationVariableCoefficientStd. Error t-StatisticProb.C7144148822046212 3.2405340.0038X*WGTA2-2711.9615055.773 -0.5364090.5971WGTA21353635120714871 0.6534610.5202R-squared0.023255Mean dependent var65232673A

16、djusted R-squared-0.065539S.D. dependent var61762160S.E. of regression63753972Akaike info criterion38.89113Sum squared resid8.94E+16Schwarz criterion39.03739Log likelihood-483.1391Hannan-Quinn criter.38.93170F-statistic0.261901Durbin-Watson stat0.898907Prob(F-statistic)0.771953修正后的模型为AY 10781.17 3.9

17、31606Xit (4.925821 )(20.47667)R2 0.9480, n 255.4 表5.4的数据是2011年各地区建筑业总产值（X）和建筑业企业利润总额（Y）。表5.4 各地区建筑业总产值（X）和建筑业企业利润总额（ Y）（单位：亿元）地区建筑业总产值X建筑业企业利润总额Y地区建筑业总产值X建筑业企业利润总额Y北京6046.22216.78湖北5586.45231.46天津2986.4579.54湖南3915.02124.77河北3972.66127.00广东5774.01251.69山西2324.9149.22广西1553.0726.24内蒙古1394.68105.37海南2

18、55.476.44辽宁6217.52224.31重庆3328.83155.34吉林1626.6589.03四川5256.65177.19黑龙江2029.1658.92贵州824.7214.39上海4586.28166.69云南1868.4061.88江苏15122.85595.87西藏124.475.75浙江14907.42411.57陕西3216.63104.38安徽3597.26127.12甘肃925.8429.33福建3692.62126.47青海319.428.35江西2095.4762.37宁夏427.9211.25山东6482.90291.77新疆1320.3727.60河南527

19、9.36200.09数据来源：国家统计局网站根据样本资料建立回归模型，分析建筑业企业利润总额与建筑业总产值的关系， 并判断 模型是否存在异方差，如果有异方差，选用最简单的方法加以修正。解：散点图:建立线性回归模型:Dependent Variable: YMethod: Least SquaresDate: 04/18/20 Time: 21:16Sample: 1 31Included observations: 31Variable iCoefficientStd. Error t-StatisticProb.C2.3681389.049371 0.2616910.7954X0.03498

20、00.001754 19.945300.0000R-squared0.932055Mean dependent var134.4574Adjusted R-squared0.929712S.D. dependent var129.5145S.E. of regression34.33673Akaike info criterion9.972649Sum squared resid34191.33Schwarz criterion10.06516Log likelihood-152.5761Hannan-Quinn criter.10.00281F-statistic397.8152Durbin

21、-Watson stat2.572841Prob(F-statistic)0.000000white检验：Heteroskedasticity Test: WhiteF-statistic26.00369Prob. F(2,28)0.0000Obs*R-squared20.15100Prob. Chi-Square(2)0.0000Scaled explained SS40.83473 Prob. Chi-Square(2)0.0000Test Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 04/18/20 Tim

22、e: 21:19Sample: 1 31Included observations: 31VariableCoefficientStd. Error t-StatisticProb.C498.3340559.4185 0.8908070.3806XA24.51E-051.45E-05 3.1106100.0043X-0.1581760.221918 -0.7127680.4819R-squared0.650032Mean dependent var1102.946Adjusted R-squared0.625035S.D. dependent var2412.791S.E. of regres

23、sion1477.458Akaike info criterion17.52580Sum squared resid61120730Schwarz criterion17.66457Log likelihood-268.6499Hannan-Quinn criter.17.57104F-statistic26.00369Durbin-Watson stat2.732318Prob(F-statistic)0.000000模型存在异方差模型修正：加权最小二乘法Dependent Variable: YMethod: Least SquaresDate: 04/18/20 Time: 21:24S

24、ample: 1 31Included observations: 31Weighting series: W2Weight type: Inverse variance (average scaling)Variable Coefficient Std. Error t-Statistic Prob.C 0.020734 1.351842 0.015338 0.9879X 0.034505 0.002445 14.11049 0.0000Weighted StatisticsR-squared 0.872866 Mean dependent var 19.08548Adjusted R-sq

25、uared0.868482S.D. dependent var6.416052S.E. of regression6.525709Akaike info criterion6.651717Sum squared resid1234.962Schwarz criterion6.744233Log likelihood-101.1016Hannan-Quinn criter.6.681875F-statistic199.1059Durbin-Watson stat2.201198Prob(F-statistic)0.000000Weighted mean dep.9.525906Unweighte

26、d StatisticsR-squared0.930826Mean dependent var134.4574Adjusted R-squared0.928441S.D. dependent var129.5145S.E. of regression34.64582Sum squared resid34809.66Durbin-Watson stat2.531761加权后进行white检验:Heteroskedasticity Test: WhiteF-statistic0.224402Prob. F(2,28)0.8004Obs*R-squared0.489051Prob. Chi-Squa

27、re(2)0.7831Scaled explained SS1.141138Prob. Chi-Square(2)0.5652Test Equation:Dependent Variable: WGT_RESIDA2Method: Least SquaresDate: 04/18/20 Time: 21:25Sample: 1 31Included observations: 31Collinear test regressors dropped from specificationVariableCoefficientStd. Error t-StatisticProb.C28.9064724.35074 1.1870880.2452X*WGTA20.0746340.111471 0.6695390.5086WGTA2-9.62870615.02003 -0.6410580.5267R-squared0.015776Mean dependent var39.83747Adjusted R-squared-0.054526S.D. depen