实验五异方差模型的检验

Documentserialnumber【UU89WT-UU98YT-UU8CB-UUUT-UUT108】Documentserialnumber【UU89WT-UU98YT-UU8CB-UUUT-UUT108】实验五异方差模型的检验实验报告课程名称：计量经济学实验项目：实验五异方差模型的检验和处理实验类型：综合性□设计性□验证性专业班别：12国姓名：学号：412实验课室：厚德楼A404指导教师：实验日期：2015年5月28日广东商学院华商学院教务处制一、实验项目训练方案小组合作：是□否小组成员：无实验目的：掌握异方差模型的检验和处理方法实验场地及仪器、设备和材料实验室：普通配置的计算机，Eviews软件及常用办公软件。实验训练内容（包括实验原理和操作步骤）：【实验原理】异方差的检验：图形检验法、Goldfeld-Quanadt检验法、White检验法、Glejser检验法；异方差的处理：模型变换法、加权最小二乘法(WLS)。【实验步骤】本实验考虑三个模型：【1】广东省财政支出CZ对财政收入CS的回归模型；（数据见附表1：附表1-广东省数据）【2】广东省固定资产折旧ZJ对国内生产总值GDPS和时间T的二元回归模型；（数据见附表1：附表1-广东省数据）【3】广东省各市城镇居民消费支出Y对人均收入X的回归模型。（数据见附表2：附表2-广东省2005年数据）（一）异方差的检验1.图形检验法分别用相关分析图和残差散点图检验模型【1】、模型【2】和模型【3】是否存在异方差。注：①相关分析图是作应变量对自变量的散点图（亦可作模型残差对自变量的散点图）；②残差散点图是作残差的平方对自变量的散点图。③模型【2】中作图取自变量为GDPS来作图。模型【1】相关分析图残差散点图模型【2】相关分析图残差散点图模型【3】相关分析图残差散点图【思考】①相关分析图和残差散点图的不同点是什么②*在模型【2】中，自变量有两个，有无其他处理方法尝试做出来。（请对得到的图表进行处理，以上在一页内）检验法用Goldfeld-Quanadt检验法检验模型【3】是否存在异方差。注：Goldfeld-Quanadt检验法的步骤为：①排序：②删除观察值中间的约1/4的，并将剩下的数据分为两个部分。③构造F统计量：分别对上述两个部分的观察值求回归模型，由此得到的两个部分的残差平方为和。为较大的残差平方和，为较小的残差平方和。④算统计量。⑤判断：给定显着性水平，查F分布表得临界值。如果，则认为模型中的随机误差存在异方差。（详见课本135页）将实验中重要的结果摘录下来，附在本页。obsXY12345678910111

12131415161718DependentVariable:YMethod:LeastSquaresDate:06/07/15Time:11:18Sample:17Includedobservations:7VariableCoefficientStd.Errort-StatisticProb.XCR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresid1757380.SchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)DependentVariable:YMethod:LeastSquaresDate:06/07/15Time:11:20Sample:1218Includedobservations:7VariableCoefficientStd.Errort-StatisticProb.XCR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)有上图可知，=1757380F=/在下，上式中分子、分母的自由度均为5，查F分布表得临界值（5,5）=，因为F=（5,5）=，所以拒接原假设，说明模型存在异方差。（请对得到的图表进行处理，以上在一页内）检验法分别用White检验法检验模型【1】、模型【2】和模型【3】是否存在异方差。Eviews操作：先做模型，选view/ResidualTests/HeteroskedasticityTests/White/(勾选crossterms)。摘录主要结果附在本页内。模型【1】HeteroskedasticityTest:WhiteF-statistic4.

40866Prob.F(2,25)Obs*R-squaredProb.Chi-Square(2)ScaledexplainedSSProb.Chi-Square(2)TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:06/07/15Time:12:44Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.CCSCS^2R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresid+08SchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)模型【2】HeteroskedasticityTest:WhiteF-statisticProb.F(5,22)Obs*R-squaredProb.Chi-Square(5)ScaledexplainedSSProb.Chi-Square(5)TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:06/07/15Time:12:47Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.CGDPSGDPS^2GDPS*TTT^2R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresid+08SchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)模型【3】HeteroskedasticityTest:WhiteF-statisticProb.F(2,15)Obs*R-squaredProb.Chi-Square(2)ScaledexplainedSSProb.Chi-Square(2)TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:06/07/15Time:12:51Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.C1865425.2810916.XX^2R-squaredMeandependentvar1232693.AdjustedR-squared.dependentvar2511199..ofregression1879689.AkaikeinfocriterionSumsquaredresid+13SchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)（请对得到的图表进行处理，以上在一页内）检验法用Glejser检验法检验模型【1】是否存在异方差。分别用残差的绝对值对自变量的一次项、二次项，开根号项和倒数项作回归。检验异方差是否存在，并选定异方差的最优形式。摘录主要结果附在本页内。一、一次项回归DependentVariable:E1Method:LeastSquaresDate:06/07/15Time:13:17Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.CSCR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)

二、去掉常数项再回归DependentVariable:E1Method:LeastSquaresDate:06/07/15Time:13:22Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.CSR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.Durbin-Watsonstat三、二次项回归DependentVariable:E1Method:LeastSquaresDate:06/07/15Time:13:19Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.CS^2CR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)四、开根号项回归DependentVariable:E1Method:LeastSquaresDate:06/07/15Time:13:24Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.CS^(1/2)R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.Durbin-Watsonstat

五、倒数项作回归DependentVariable:E1Method:LeastSquaresDate:06/07/15Time:13:26Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.CS^(-1)CR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)

从四个回归的结果看，第二个不显着，其他三个显着，比较这三个回归，还是选择第三个，方程为即异方差的形式为：σ2=（*（CS^(1/2)））2=也即异方差的形式为：σ2=σ2CS就把这个形式确定为异方差的形式。对ZJ与GDPS和T回归的Glejser检验可以类似进行检验，消费支出与可支配收入回归的Glejser检验可以类似进行检验。

通过前面实验的异方差模型的检验，发现根据广东数据CZ对CS的回归，ZJ对GDPS和T的回归，消费支出与可支配收入回归都存在异方差，现在分别对它们进行处理。加权最小二乘法已经成为处理异方差模型的标准方法，再Eviews中使用WLS来消除异方差，关键是权数的选取。（请对得到的图表进行处理，以上在一页内）（二）异方差的处理1.模型【1】中CZ对CS回归异方差的处理已知CZ对CS回归异方差的形式为：，选取权数，使用加权最小二乘法处理异方差。并检验处理异方差之后模型是否仍存在异方差，若仍然存在异方差，请继续处理异方差。摘录主要结果附在本页内。DependentVariable:CZMethod:LeastSquaresDate:06/07/15Time:13:32Sample:19782005Includedobservations:28Weightingseries:1/(CS^(1/2))VariableCoefficientStd.Errort-StatisticProb.CSCWeightedStatisticsR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)UnweightedStatisticsR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionSumsquaredresidDurbin-Watsonstat

回归方程为它与存在异方差的如下方程估计有所不同。至于经过加权最小二乘法估计的残差项是否存在异方差，同样可以用本实验的异方差模型的检验去检验，但是若在eviews中使用wls命令估计的序列resed不能用俩检验，因为产生的序列resid是非加权方式的残差。要想检验只能自己进行同方差变换，然后回归以后再检验了。进行同方差行变换，然后回归实际上就是CZ/(CS^(1/2)对1/(CS^(1/2))和CS/(CS^(1/2)回归，结果如下：DependentVariable:CZ/(CS^(1/2))Method:LeastSquaresDate:06/07/15Time:13:39Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.1/(CS^(1/2))CS/(CS^(1/2))R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.Durbin-Watsonstat

观察其残差趋势图还是存在异方差，再改为CZ/CS对1/CS和回归，如果如下:DependentVariable:CZ/CSMethod:LeastSquaresDate:06/07/15Time:13:42Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.1/CSCR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)观察其残差趋势图（请对得到的图表进行处理，以上在两页内）2.模型【2】中ZJ对GDPS和T回归异方差的处理已知ZJ对GDPS和T回归异方差的形式为：，选取权数，使用加权最小二乘法处理异方差。并检验处理异方差之后模型是否仍存在异方差，若仍然存在异方差，请继续处理异方差。摘录主要结果附在本页内。DependentVariable:ZJMethod:LeastSquaresDate:06/07/15Time:13:46Sample:19782005Includedobservations:28Weightingseries:1/(GDPS^(3/8))VariableCoefficientStd.Errort-StatisticProb.GDPSTWeightedStatisticsR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.Durbin-WatsonstatUnweightedStatisticsR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionSumsquaredresidDurbin-Watsonstat它与存在异方差时的如下方程估计也有所不同。进行同方差性变换，然后回归实际上就是ZJ/(GDPS^(8/3))对GDPS/(GDPS^(8/3))和T/(GDPS^(8/3)回归，结果如下：DependentVariable:ZJ/(GDPS^(3/8))Method:LeastSquaresDate:06/07/15Time:13:50Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.GDPS/(GDPS^(3/8))T/(GDPS^(3/8))R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.Durbin-Watsonstat观测其残差趋势图可能还存在异方差，再改为ZJ/GDPS对C和T/GDPS回归，结果如下：DependentVariable:ZJ/GDPSMethod:LeastSquaresDate:06/07/15Time:13:52Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.CT/GDPSR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)

观测其残差趋势图应该不存在异方差了，其方程为变换为原方程（请对得到的图表进行处理，以上在两页内）3.模型【3】中消费支出Y对可支配收入X回归异方差的处理已知Y对X回归异方差的形式为：，选取权数，使用加权最小二乘法处理异方差。并检验处理异方差之后模型是否仍存在异方差，若仍然存在异方差，请继续处理异方差。摘录主要结果附在本页内。DependentVariable:YMethod:LeastSquaresDate:06/07/15Time:13:56Sample:118Includedobservations:18Weightingseries:1/X^(2/3)VariableCoefficientStd.Errort-StatisticProb.XWeightedStatisticsR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.Durbin-WatsonstatUnweightedStatisticsR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionSumsquaredresidDurbin-Watsonstat

它与存在异方差时如下方程估计明显不同进行同方差性变换，然后回归实际上就是Y/(X^(2/3))和X/(X^(2/3))回归，结果如下：DependentVariable:Y/(X^(2/3))Method:LeastSquaresDate:06/07/15Time:13:59Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.1/(X^(2/3))X/(X^(2/3))R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.Durbin-Watsonstat观测其残差趋势图虽然不能够准确判断，但大致还是存