1、例4.2.1 中國居民總量消費函數注意：本例的數據是表2.6.3后三列 x、y、t本例任務：1、 建立模型，導入數據2、進行最小二乘回歸3、將上述最小二乘回歸的殘差保存下來，4、序列相關檢驗-圖示檢驗法（包括殘差時間圖、殘差散點圖）5、在原模型中增加時間趨勢項T2：（p教材132頁4.2.24式）6、拉格朗日乘數檢驗7、序列相關修正廣義差分法（一階差分）8、序列相關修正序列相關穩健標準誤法任務開始：1、建立模型，導入數據輸入命令： data x y t 將數據復制粘貼進去2、進行最小二乘回歸： 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-squared0.987955    Mean dependent var14855.72Adjusted R-squared0.987509   &

3、#160;S.D. dependent var9472.076S.E. of regression1058.633    Akaike info criterion16.83382Sum squared resid30259014    Schwarz criterion16.92811Log likelihood-242.0903    Hannan-Quinn criter.16.86335F-statistic2214.596   

4、0;Durbin-Watson stat0.277155Prob(F-statistic)0.000000Y對X做最小二乘回歸的結果（p教材132頁4.2.23式）：3、將上述最小二乘回歸的殘差保存下來，genr e=resid 4、進行序列相關性檢驗圖示檢驗法：（1）作殘差-時間圖直接在回歸方程Equation窗口點擊viewgraph-（或者直接在命令框中輸入命令 line e ）（2）作殘差相關圖直接在命令框輸入 scat e (-1) e 即可快捷鍵（或者在主標題欄點擊快捷鍵QuickGraph輸入e(-1) e也可以）可以對圖形格式進行設置，雙擊圖形：設置顏色、線型、線粗、符號標簽等

5、，變成與教材中一致的圖形：設置坐標軸格式:將左側和底側坐標軸加上0線對左邊坐標軸進行設置坐標軸標簽在圖形底層加上0線對底邊的找坐標軸進行設置加上0線得到如下圖形：5、增加時間趨勢項以后的模型：（p教材132頁4.2.24式）ls y c x t2Dependent Variable: YMethod: Least SquaresDate: 11/24/14 Time: 11:45Sample: 1978 2006Included observations: 29VariableCoefficientStd. Errort-StatisticProb.  C3328.1911

6、95.032617.064790.0000X0.1761520.0259866.7787880.0000T221.655822.12418310.194890.0000R-squared0.997590    Mean dependent var14855.72Adjusted R-squared0.997404    S.D. dependent var9472.076S.E. of regression482.5729    Akaike info criterion15

7、.29384Sum squared resid6054792.    Schwarz criterion15.43528Log likelihood-218.7607    Hannan-Quinn criter.15.33814F-statistic5380.771    Durbin-Watson stat0.442033Prob(F-statistic)0.000000根據回歸結果進行DW檢驗：D-W統計量的值為 0.442033，存在正相關。6、拉格朗日乘數檢驗：首先

8、，做輔助回歸模型（p教材133頁，含1階滯后殘差項的輔助回歸）。在命令框輸入點擊回車鍵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-47.00080122.0208-0.3851870.7

9、035X0.0190910.0161921.1790790.2499T2-1.6186551.325944-1.2207560.2340E(-1)0.7606140.1223446.2170100.0000R-squared0.618910    Mean dependent var25.70108Adjusted R-squared0.571274    S.D. dependent var452.0910S.E. of regression296.0164    Akai

10、ke info criterion14.35027Sum squared resid2103016.    Schwarz criterion14.54058Log likelihood-196.9038    Hannan-Quinn criter.14.40845F-statistic12.99243    Durbin-Watson stat1.426529Prob(F-statistic)0.000030LM=n*擬合優度=28*0.618910=17.33大于臨界值

11、，由此判斷原模型存在1階序列相關性。接下來，做二階序列相關檢驗（p教材133頁，含2階滯后殘差項的輔助回歸）在命令框輸入ls e c x t2 e(-1) e(-2) 點擊回車鍵Dependent Variable: EMethod: Least SquaresDate: 11/24/14 Time: 12:30Sample (adjusted): 1980 2006Included observations: 27 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.  C-61.20279120.4

12、509-0.5081140.6164X0.0173600.0157341.1033630.2818T2-1.4202531.295108-1.0966290.2847E(-1)1.0563720.2000115.2815570.0000E(-2)-0.3628410.191018-1.8995100.0707R-squared0.656677    Mean dependent var44.12864Adjusted R-squared0.594255    S.D. dependent var449.8594S.

13、E. of regression286.5520    Akaike info criterion14.31929Sum squared resid1806465.    Schwarz criterion14.55926Log likelihood-188.3105    Hannan-Quinn criter.14.39065F-statistic10.51991    Durbin-Watson stat1.994011Prob(

14、F-statistic)0.000064LM=n*擬合優度=27*0.656677=17.7大于臨界值，由此判斷原模型存在序列相關性，但是殘差滯后兩階項E(-2)沒通過5%的顯著性檢驗，說明不存在2階序列相關。7、運用廣義差分法進行序列相關的修正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

15、after 5 iterationsVariableCoefficientStd. Errort-StatisticProb.  C3505.737403.32768.6920350.0000X0.1995350.0302636.5933220.0000T219.242082.9268336.5743700.0000AR(1)0.7479220.1260425.9338930.0000R-squared0.999093    Mean dependent var15250.33Adjusted R-squared0.998979

16、60;   S.D. dependent var9400.011S.E. of regression300.2877    Akaike info criterion14.37892Sum squared resid2164144.    Schwarz criterion14.56924Log likelihood-197.3049    Hannan-Quinn criter.14.43710F-statistic8811.099 

17、   Durbin-Watson stat1.394889Prob(F-statistic)0.000000Inverted AR Roots      .75回歸結果輸出為： = 3505.73736684 + 0.199534620068*X + 19.2420790771*T2 + 0.747922 AR(1)（p教材133頁4.2.25式）AR(1)前的參數即為隨機擾動項的1階序列相關系數。N=28,k=4在5%的顯著性水平下，D-W統計量的上下限為1.18和1.65，而D-W統計量的值為1.394889，無法判斷經廣義差分變換后的模型是否已不存在序列相關，因此再采用LM檢驗去判斷：首先重新保存殘差序列 genr e=r