计量经济学课件第五章复习进程

7791857529.

19003600014.

8191953530.

21003620015.

12222116331.

23003820016.

170222880

HebeiUniversityofTechnologyHebeiUniversityofTechnology戈特菲尔德—夸特检验

适用条件：（1）大样本（n）30）；（2）观测值至少应为参数个数的2倍；（3）随机项无自相关且服从正态分布（4）具有递增或递减方差

HebeiUniversityofTechnology1.建立假设：原假设：是同方差的；备择假设：是异方差的。2.处理观测值3.建立回归方程求残差平方和4.计算F统计量5.结论HebeiUniversityofTechnology7.2621.6205.552318.45720.20032.38018.46.224226.578020.76640.14291.52169.6726.4217.603823.07560.36454.308310.8930238.629526.53940.137212.5278121032.4309.655228.84860.11881.325513.210.5363410.680932.31250.03272.8476合计0.996724.9111HebeiUniversityofTechnology所以数据存在异方差性。

HebeiUniversityofTechnology斯皮尔曼等级相关法

1.原模型应用OLS法，计算残差2.计算的等级差3.计算等级相关系数4.总体等级相关系数进行显著性检验5.于给定显著性水平,如果，则拒绝原假设，接受备择假设。否则拒绝备择假设，接受原假设。HebeiUniversityofTechnology17.265.30220.697717-63628.46.26.37510.1751220039.677.44790.447934-11410.898.52080.479145-11512109.59360.40635324613.210.510.66640.166461525714.411.211.73930.53937611815.61212.81210.81218800918.01414.95780.975899001021.62018.17631.82361012-2411242220.32201.67791111001226.42122.46771.467712102413302325.68622.68621314-111432.43027.83192.168014131115363431.05042.9495151500HebeiUniversityofTechnology

所以数据存在异方差性。HebeiUniversityofTechnology怀特检验法

1.首先用普通最小二乘法估计回归方程，得残差2.然后作如下回归：3.求辅助方程的原假设下4.如果超过临界值，则认为存在异方差。HebeiUniversityofTechnologyF-statistic7.864555Probability0.001947TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:07/21/02Time:21:24Sample:131C12757.9069326.780.1840260.8553SER02-1.1824976.787256-0.1742230.8629R-squared0.359694Meandependentvar57256.95AdjustedR-squared0.313958S.D.dependentvar68345.62S.E.ofregression56609.07Akaikeinfocriterion24.81749Sumsquaredresid8.97E+10Schwarzcriterion24.95626Loglikelihood-381.6711F-statistic7.864555WhiteHeteroskedasticityTest:Obs*R-squared11.15052Probability0.003790Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.SER02^20.0001210.0001470.8233280.4173Durbin-Watsonstat1.839878Prob(F-statistic)0.001947HebeiUniversityofTechnology帕克检验法

1.建立回归方程，并计算的残差平方2.取异方差的函数形式为：两边取对数得3.建立方差结构回归模型4.对进行t检验。HebeiUniversityofTechnologyDependentVariable:LOG(GT)Method:LeastSquaresDate:07/21/02Time:21:32Sample:131LOG(SER02)2.3379550.5807424.0258060.0004R-squared0.358508Meandependentvar10.05525AdjustedR-squared0.336388S.D.dependentvar1.795184S.E.ofregression1.462400Akaikeinfocriterion3.660376Sumsquaredresid62.01983Schwarzcriterion3.752892Loglikelihood-54.73583F-statistic16.20711Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.C-13.144165.768659-2.2785470.0302Durbin-Watsonstat1.845645Prob(F-statistic)0.000373HebeiUniversityofTechnology格莱泽检验

建立被解释变量y对所有解释变量的回归方程，然后计算残差利用OLS法对上述函数进行估计，得回归方程。并计算每个回归方程的拟合优度，把拟合优度最大的作为最佳拟合的回归形式。对最佳线性中的参数进行显著性检验。HebeiUniversityofTechnology巴特列特检验

见张寿、于清文著《计量经济学》166页。HebeiUniversityofTechnologyBreusch—pagan检验

是一种较好的检验方法，可以检验有多个解释变量引起的异方差的情况，详细的讨论见赵国庆著《计量经济学》115页。

其他的检验还有：CUSUM、CUSUMSQ等，详细讨论见有关参考书。但在实际应用中，人们并不经常使用这些检验方法，更多的是从经济背景方面去分析与判断是否可能存在异方差性，如果可能，则选用适当的方法去估计模型的参数。

HebeiUniversityofTechnology第四节异方差问题的解决方法

HebeiUniversityofTechnology广义最小二乘法原模型为当，当其它假定都满足时，

HebeiUniversityofTechnology一定存k阶在非奇异矩阵P，使利用矩阵P来变换模型：令，则因此变换后的模型满足同方差和无自相关假定。HebeiUniversityofTechnology广义最小二乘估计量的统计特性

线性性

HebeiUniversityofTechnology无偏性HebeiUniversityofTechnology有效性TheGauss-MarkovTheorem:theGLSestimatoristhebestlinearunbiasedestimator(BLUE)amongallpossiblelinearunbiasedestimator,theGLSestimatoristhebestonewiththesmallestvariance.HebeiUniversityofTechnology已知的情况（加权最小二乘法）

HebeiUniversityofTechnology未知的情况

HebeiUniversityofTechnologyHebeiUniversityofTechnologyDependentVariable:Y/XMethod:LeastSquaresDate:07/21/02Time:21:49Sample:131B0-722.686172.28227-9.9981100.0000R-squared0.775128Meandependentvar0.048768AdjustedR-squared0.767374S.D.dependentvar0.021761S.E.ofregression0.010496Akaikeinfocriterion-6.213380Sumsquaredresid0.003195Schwarzcriterion-6.120865Loglikelihood98.30739F-statistic99.96220Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.B10.0881620.00436820.184150.0000Durbin-Watsonstat0.993129Prob(F-statistic)0.000000HebeiUniversityofTechnologyWhite异方差修正一致估计量

HebeiUniversityofTechnologyDependentVariable:SER01Method:LeastSquaresDate:07/21/02Time:21:52Sample:131Includedobservations:31SER020.0846630.00527216.058410.0000R-squared0.912210Meandependentvar