例421操作步骤及结果

1、例4.2.1 中国居民总量消费函数注意：本例的数据是表2.6.3后三列 x、y、t本例任务：1、 建立模型，导入数据2、进行最小二乘回归3、将上述最小二乘回归的残差保存下来，4、序列相关检验-图示检验法（包括残差时间图、残差散点图）5、在原模型中增加时间趋势项T2：（p教材132页4.2.24式）6、拉格朗日乘数检验7、序列相关修正广义差分法（一阶差分）8、序列相关修正序列相关稳健标准误法任务开始：1、建立模型，导入数据输入命令： data x y t 将数据复制粘贴进去2、进行最小二乘回归： ls y c x Dependent Variable: YMethod: Least Square

2、sDate: 11/24/14 Time: 10:48Sample: 1978 2006Included observations: 29VariableCoefficientStd. Errort-StatisticProb.C2091.295334.98696.2429140.0000X0.4375270.00929747.059500.0000R-squared0.987955Mean dependent var14855.72Adjusted R-squared0.987509S.D. dependent var9472.076S.E. of regression1058.633Aka

3、ike info criterion16.83382Sum squared resid30259014Schwarz criterion16.92811Log likelihood-242.0903Hannan-Quinn criter.16.86335F-statistic2214.596Durbin-Watson stat0.277155Prob(F-statistic)0.000000Y对X做最小二乘回归的结果（p教材132页4.2.23式）：3、将上述最小二乘回归的残差保存下来，genr e=resid 4、进行序列相关性检验图示检验法：（1）作残差-时间图直接在回归方程Equatio

4、n窗口点击viewgraph-（或者直接在命令框中输入命令 line e ）（2）作残差相关图直接在命令框输入 scat e (-1) e 即可快捷键（或者在主标题栏点击快捷键QuickGraph输入e(-1) e也可以）可以对图形格式进行设置，双击图形：设置颜色、线型、线粗、符号标签等，变成与教材中一致的图形：设置坐标轴格式:将左侧和底侧坐标轴加上0线对左边坐标轴进行设置坐标轴标签在图形底层加上0线对底边的找坐标轴进行设置加上0线得到如下图形：5、增加时间趋势项以后的模型：（p教材132页4.2.24式）ls y c x t2Dependent Variable: YMethod: Leas

5、t SquaresDate: 11/24/14 Time: 11:45Sample: 1978 2006Included observations: 29VariableCoefficientStd. Errort-StatisticProb.C3328.191195.032617.064790.0000X0.1761520.0259866.7787880.0000T221.655822.12418310.194890.0000R-squared0.997590Mean dependent var14855.72Adjusted R-squared0.997404S.D. dependent

6、var9472.076S.E. of regression482.5729Akaike info criterion15.29384Sum squared resid6054792.Schwarz criterion15.43528Log likelihood-218.7607Hannan-Quinn criter.15.33814F-statistic5380.771Durbin-Watson stat0.442033Prob(F-statistic)0.000000根据回归结果进行DW检验：D-W统计量的值为 0.442033，存在正相关。6、拉格朗日乘数检验：首先，做辅助回归模型（p教材

7、133页，含1阶滞后残差项的辅助回归）。在命令框输入点击回车键genr e=resid ls e c x t2 e(-1) Dependent Variable: EMethod: Least SquaresDate: 11/24/14 Time: 12:25Sample (adjusted): 1979 2006Included observations: 28 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C-47.00080122.0208-0.3851870.7035X0.0190910.0161921.17

8、90790.2499T2-1.6186551.325944-1.2207560.2340E(-1)0.7606140.1223446.2170100.0000R-squared0.618910Mean dependent var25.70108Adjusted R-squared0.571274S.D. dependent var452.0910S.E. of regression296.0164Akaike info criterion14.35027Sum squared resid2103016.Schwarz criterion14.54058Log likelihood-196.90

9、38Hannan-Quinn criter.14.40845F-statistic12.99243Durbin-Watson stat1.426529Prob(F-statistic)0.000030LM=n*拟合优度=28*0.618910=17.33大于临界值，由此判断原模型存在1阶序列相关性。接下来，做二阶序列相关检验（p教材133页，含2阶滞后残差项的辅助回归）在命令框输入ls e c x t2 e(-1) e(-2) 点击回车键Dependent Variable: EMethod: Least SquaresDate: 11/24/14 Time: 12:30Sample (adj

10、usted): 1980 2006Included observations: 27 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C-61.20279120.4509-0.5081140.6164X0.0173600.0157341.1033630.2818T2-1.4202531.295108-1.0966290.2847E(-1)1.0563720.2000115.2815570.0000E(-2)-0.3628410.191018-1.8995100.0707R-squared0.656677Mean dep

11、endent var44.12864Adjusted R-squared0.594255S.D. dependent var449.8594S.E. of regression286.5520Akaike info criterion14.31929Sum squared resid1806465.Schwarz criterion14.55926Log likelihood-188.3105Hannan-Quinn criter.14.39065F-statistic10.51991Durbin-Watson stat1.994011Prob(F-statistic)0.000064LM=n

12、*拟合优度=27*0.656677=17.7大于临界值，由此判断原模型存在序列相关性，但是残差滞后两阶项E(-2)没通过5%的显著性检验，说明不存在2阶序列相关。7、运用广义差分法进行序列相关的修正ls y c x t2 ar(1)Dependent Variable: YMethod: Least SquaresDate: 11/24/14 Time: 12:38Sample (adjusted): 1979 2006Included observations: 28 after adjustmentsConvergence achieved after 5 iterationsVariab

13、leCoefficientStd. Errort-StatisticProb.C3505.737403.32768.6920350.0000X0.1995350.0302636.5933220.0000T219.242082.9268336.5743700.0000AR(1)0.7479220.1260425.9338930.0000R-squared0.999093Mean dependent var15250.33Adjusted R-squared0.998979S.D. dependent var9400.011S.E. of regression300.2877Akaike info

14、 criterion14.37892Sum squared resid2164144.Schwarz criterion14.56924Log likelihood-197.3049Hannan-Quinn criter.14.43710F-statistic8811.099Durbin-Watson stat1.394889Prob(F-statistic)0.000000Inverted AR Roots.75回归结果输出为： = 3505.73736684 + 0.199534620068*X + 19.2420790771*T2 + 0.747922 AR(1)（p教材133页4.2.25式）AR(1)前的参数即为随机扰动项的1阶序列相关系数。N=28,k=4在5%的显著性水平下，D-W统计量的上下限为1.18和1.65，而D-W统计量的值为1.394889，无法判断经广义差分变换后的模型是否已不存在序列相关，因此再采用LM检验去判断：首先重新保存残差序列 genr e=resid然后做LM检验的辅助回归方程：ls e c x-0.747922*x(-1