1、大连海事大学计量经济学Eviews实验课讲义5序列相关与异方差上机课第五课 序列相关与异方差模型的处理5.1序列相关模型一、首先，结合案例数据（5_1_1）研究天津市城镇居民人均消费与人均可支配收入的关系，分析一阶线性相关存在时模型的检验与处理。（1）案例数据：改革开放以来，天津市城镇居民人均消费性支出（CONSUM），人均可支配收入（INCOME）以及消费价格指数（PRICE）数据（19782000年）见下表。（数据来源：张晓峒，计量经济学基础，P152，例6.1）（2）散点图考虑到价格指数的影响，将CONSUM和INCOME各自除以价格指数，形成被解释变量和解释变量：CONSUM/PRIC
2、E和INCOME/PRICE，并作散点图如下，分析散点图，CONSUM/PRICE和INCOME/PRICE呈现线性相关。（3）回归结果，Eviews输出结果报告，得到回归方程CONSUM/PRICE = 111.4400081 + 0.7118287831*INCOME/PRICEDependent Variable: CONSUM/PRICEVariableCoefficientStd. Errort-StatisticProb.C111.440017.055926.5338040.0000INCOME/PRICE0.7118290.01689942.122210.0000R-square
3、d0.988303Mean dependent var769.4035Adjusted R-squared0.987746S.D. dependent var296.7204S.E. of regression32.84676Akaike info criterion9.904525Sum squared resid22657.10Schwarz criterion10.00326Log likelihood-111.9020F-statistic1774.281Durbin-Watson stat0.598571Prob(F-statistic)0.000000水平上，T=23条件下，k=1
4、时，临界值Dl=1.26，由结果可知，DW=0.59,因此，拒绝零假设，认为存在一阶序列相关。0.678967说明存在正相关。（5）用广义最小二乘法估计参数计算一阶相关系数,对原变量做广义差分，若令,令, ,则以和为样本再次计算回归方程，GDY = 45.24890183 + 0.6782321994*GDXDependent Variable: GDYIncluded observations: 22 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C45.2489012.258623.6911910.0014GDX
5、0.6782320.03398319.957990.0000R-squared0.952190Mean dependent var269.1295Adjusted R-squared0.949799S.D. dependent var103.4908S.E. of regression23.18764Akaike info criterion9.211624Sum squared resid10753.33Schwarz criterion9.310809Log likelihood-99.32786F-statistic398.3214Durbin-Watson stat2.308815Pr
6、ob(F-statistic)0.000000DW值=2.34-du=4-1.43=2.57，已经消除序列相关。由于，因此原模型的估计结果为：。分析可知，天津市城镇居民人均消费性支出平均占人均可支配收入的67.82%。注意：对广义差分后模型与原模型的判定系数不可简单直接比较，因为其变量不同；两个模型的回归系数估计值可能有所不同，计量经济学理论认为，广义差分模型的估计量性质优于存在序列相关时模型的估计量。Eviews操作：生成新变量的方法：QuickGenerate Series“X=CONSUM/PRICE”、”INCOME/PRICE”,但每次只能收入一个命令；LM(BG)检验方法：Equa
7、tionViewsResidual TestsSerial Correlation LMTestOK。二、结合案例5_1_2，研究天津市保费收入和人口的回归关系，分析二阶序列相关存在时模型的检验与处理。（1） 天津市保费收入和人口数据：19671978年天津市的保险费收入（Yt，万元）和人口（Xt，万人）数据见5_1_2，散点图见下图，Y与X呈指数关系，对Y对自然对数，LnY与X呈线性关系。（数据来源：张晓峒，计量经济学基础，P155,例6.2）（2）散点图： 通过散点图确定模型形式： （3）利用Eviews软件估计方程，得到LOG(Y) = -11.18098138 + 0.02540509
8、726*X输出结果为：Dependent Variable: LOG(Y)Included observations: 32VariableCoefficientStd. Errort-StatisticProb.C-11.180980.534786-20.907400.0000X0.0254050.00068337.209290.0000R-squared0.978792Mean dependent var8.591552Adjusted R-squared0.978085S.D. dependent var2.300249S.E. of regression0.340525Akaike i
9、nfo criterion0.743808Sum squared resid3.478727Schwarz criterion0.835416Log likelihood-9.900921F-statistic1384.531Durbin-Watson stat0.363124Prob(F-statistic)0.000000对模型结果分析，判定系数较大，0.98，拟合较好，系数显著，但是DW值较小，怀疑有自相关。（4）检验自相关查表，n=32，k=1,，Dl=1.37，Du=1.50，而DW=0.361.37，存在正的序列相关。Eviews下的LM检验：Breusch-Godfrey Ser
10、ial Correlation LM Test:F-statistic33.13129Prob. F(2,28)0.000000Obs*R-squared22.49464Prob. Chi-Square(2)0.000013辅助回归：Test Equation:Dependent Variable: RESIDIncluded observations: 32Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb.C-0.0846620.315807-0.
11、2680810.7906X0.0001160.0004060.2868600.7763RESID(-1)1.1732040.1740766.7396070.0000RESID(-2)-0.4421490.200364-2.2067230.0357R-squared0.702957Mean dependent var-4.66E-15Adjusted R-squared0.671131S.D. dependent var0.334988S.E. of regression0.192106Akaike info criterion-0.345072Sum squared resid1.033330
12、Schwarz criterion-0.161855Log likelihood9.521154F-statistic22.08752Durbin-Watson stat1.956428Prob(F-statistic)0.000000从检验结果看，误差项存在二阶自相关。（5）广义差分法消除自相关依据残差自回归结果：Dependent Variable: ETSample (adjusted): 1969 1998Included observations: 30 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.ET(
13、-1)1.1860050.1711456.9298240.0000ET(-2)-0.4666670.186755-2.4988160.0186R-squared0.706585Mean dependent var-0.016275Adjusted R-squared0.696106S.D. dependent var0.339942S.E. of regression0.187399Akaike info criterion-0.446816Sum squared resid0.983312Schwarz criterion-0.353403Log likelihood8.702236Durb
14、in-Watson stat1.971666得到辅助回归方程为：ET = 1.186004684*ET(-1) - 0.46666712*ET(-2)进而得到二阶相关系数,对原变量做广义差分，若令, ,则以和为样本再次计算回归方程，Dependent Variable: GDLNYMethod: Least SquaresSample (adjusted): 1969 1998Included observations: 30 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C-3.2462710.323473-10.
15、035690.0000GDX0.0258660.00144117.944590.0000R-squared0.920002Mean dependent var2.525873Adjusted R-squared0.917145S.D. dependent var0.649829S.E. of regression0.187050Akaike info criterion-0.450536Sum squared resid0.979660Schwarz criterion-0.357123Log likelihood8.758046F-statistic322.0083Durbin-Watson
16、 stat1.993633Prob(F-statistic)0.000000从结果看，DW=1.99，序列相关消除。根据计算公式：，因此，原模型的广义最小二乘估计结果为：与原估计结果LOG(Y) = -11.18098138 + 0.02540509726*X 相比，稍有差别，计量经济学理论认为广义最小二乘估计量的特性优于误差项存在自相关条件下的最小二乘估计量的特性，即0.0259比0.0254更可信，其经济含义为：每增加1万人，保费收入的对数值增加0.0259.5.2异方差模型一、案例分析（1）数据：已知某地区的个人储蓄Y，可支配收入X的截面样本数据见5_2_1，建立它们之间的线性回归模型并
17、估计（数据来源：张晓峒，计量经济学基础，P125，例5.1,该数据来源摘自【英】A.科苏扬尼斯著，许开甲等译经济计量学理论经济计量方法概述上册）。（2）建立模型根据经济理论确定计量经济学模型基本形式为，估计方程为：Y = -700.4109607 + 0.08783115594*XEviews输出结果报告如下：Dependent Variable: YMethod: Least SquaresSample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb.C-700.4110116.6679-6
18、.0034580.0000X0.0878310.00482718.195750.0000R-squared0.919464Mean dependent var1266.452Adjusted R-squared0.916686S.D. dependent var846.7570S.E. of regression244.4088Akaike info criterion13.89790Sum squared resid1732334.Schwarz criterion13.99042Log likelihood-213.4175F-statistic331.0852Durbin-Watson
19、stat1.089829Prob(F-statistic)0.000000（2）异方差检验考虑到横截面数据的特点，怀疑会产生异方差问题，对其以各种方法进行检验。简单观察noXEnoXE18777193.51691724127159.308729210-3.513991825604105.58239954-83.86041926500-227.115410508-91.51882026760179.0492510979-141.8872128300414.7892611912-238.8342227430308.2024712747-13.17282329560209.12281349917.7
20、78192428150-172.036914269-121.8522532100131.03091015522-74.90422632500265.89841116730128.99572735250174.3627121766399.049252833500-521.9331318575-152.0532936000-561.5111419635-205.1543036200-379.077152116363.640213138200145.26081622880392.8341通过对X与残差的观察，发现e似乎随着X变化而变化，怀疑有异方差，于是以各种方法对其进行检验。图示法分别绘制Y及残差
21、与解释变量X的散点图，从散点图来看，随着可支配收入的增加，Y和残差的离散程度在增加，可见随机误差项存在异方差。戈德菲尔德-匡特(Goldfeld-Quandt,G-Q)检验将X的样本观察值按照升序排列，Y的观察值顺序与X观察值对应。略去中间的9个样本观察值，剩余的样本观察值平均分为两组子样本，每个子样本的样本观察值数量为11个。分别用两个子样本进行回归，得到各自的结果报告，从而得到各自的残差平方和。A.排序noYXnoYX1264.008777.00171578.0024127.002105.009210.00181654.0025604.00390.009954.00191400.00265
22、00.004131.0010508.00201829.0026760.005122.0010979.00212017.0027430.006107.0011912.00221600.0028150.007406.0012747.00232200.0028300.008503.0013499.00242105.0029560.009431.0014269.00252250.0032100.0010588.0015522.00262420.0032500.0011898.0016730.00271720.0033500.0012950.0017663.00282570.0035250.001377
23、9.0018575.00291900.0036000.0014819.0019635.00302100.0036200.00151222.0021163.00312800.0038200.00161702.0022880.00B.划分子样本并回归子样本1：noYX1264.008777.002105.009210.00390.009954.004131.0010508.005122.0010979.006107.0011912.007406.0012747.008503.0013499.009431.0014269.0010588.0015522.0011898.0016730.00子样本2：noYX212017.0027430.00221600.00
