1、第六章自相關習題參考答案練習題6.1參考解答:（）建立回歸模型，回歸結果如下：Dependent Variable: YMethod: Least SquaresDate: 05/06/10 Time: 22:58Sample: 1960 1995Included observations: 36CoefficientStd. Errort-StatisticProb.X0.9358660.007467125.34110.0000C-9.4287452.504347-3.7649510.0006R-squared0.997841Mean dependent var289.9444Adjuste

2、d R-squared0.997777S.D. dependent var95.82125S.E. of regression4.517862Akaike info criterion5.907908Sum squared resid693.9767Schwarz criterion5.995881Log likelihood-104.3423Hannan-Quinn criter.5.938613F-statistic15710.39Durbin-Watson stat0.523428Prob(F-statistic)0.000000估計結果如下Se = (2.5043) (0.0075)t

3、 = (-3.7650)(125.3411)R2 = 0.9978，F = 15710.39，d f = 34，DW = 0.5234（）對樣本量為36、一個解釋變量的模型、5%顯著水平，查DW統計表可知，dL=1.411，dU= 1.525，模型中DW dU，說明廣義差分模型中已無自相關。同時，判定系數R2、t、F統計量均達到理想水平。由差分方程式可以得出：所以最終的消費模型為：由上述模型可知，美國個人實際可支配收入每增加1元，個人實際消費支出平均增加0.9484元。練習題6.2參考解答：（1） 模型1中存在自相關，模型2中不存在自相關。（2） 通過DW檢驗可以判定自相關的存在；在模型1中，

4、DW=0.8252，查5%顯著水平的DW統計表可知，因此模型1存在正自相關；而在模型2中，DW=1.82,查5%顯著水平的DW統計表可知，因此模型2不存在自相關。（3） 虛假自相關是由模型設定失誤所造成的自相關，主要包括遺漏某些重要的解釋變量或者模型函數形式不正確，因此在區分虛假自相關和真正自相關是主要從這兩個方面來判斷，即根據經濟意義檢查解釋變量是否遺漏了重要的變量，或者根據數據的數字特征檢驗模型形式的設定是否恰當。練習題6.3參考解答：（）先對數據進行處理，收入-消費模型（個人實際收入與個人實際消費支出）個人實際消費支出=人均生活消費支出/商品零售物價指數*100建立回歸模型，回歸結果如下

5、：Dependent Variable: YMethod: Least SquaresDate: 05/06/10 Time: 23:20Sample: 2001 2019Included observations: 19CoefficientStd. Errort-StatisticProb.X0.6904880.01287753.620680.0000C79.9300412.399196.4463900.0000R-squared0.994122Mean dependent var700.2747Adjusted R-squared0.993776S.D. dependent var246

6、.4491S.E. of regression19.44245Akaike info criterion8.872095Sum squared resid6426.149Schwarz criterion8.971510Log likelihood-82.28490Hannan-Quinn criter.8.888920F-statistic2875.178Durbin-Watson stat0.574663Prob(F-statistic)0.000000估計結果如下（）DW0.575，對樣本量為36、一個解釋變量的模型、5%顯著水平的DW統計表可知，說明誤差項存在正自相關。（）采用廣義差分

7、法使用普通最小二乘法估計的估計值，得由上式可知=0.657352，對原模型進行廣義差分，得到廣義差分方程：回歸結果如下：Dependent Variable: Y-0.657352*Y(-1)Method: Least SquaresDate: 05/06/10 Time: 23:25Sample (adjusted): 2002 2019Included observations: 18 after adjustmentsCoefficientStd. Errort-StatisticProb.C35.977618.1035464.4397370.0004X-0.657352*X(-1)0.

8、6686950.02064232.395120.0000R-squared0.984983Mean dependent var278.1002Adjusted R-squared0.984044S.D. dependent var105.1781S.E. of regression13.28570Akaike info criterion8.115693Sum squared resid2824.158Schwarz criterion8.214623Log likelihood-71.04124Hannan-Quinn criter.8.129334F-statistic1049.444Du

9、rbin-Watson stat1.830746Prob(F-statistic)0.000000估計結果如下DW=1.830，已知，模型中因此，在廣義差分模型中已無自相關。由差分方程式可以得出：（錯誤）（正確）因此，修正后的回歸模型應為由上述模型可知，個人實際收入每增加1元，個人實際支出平均增加0.668695元。6.4參考答案1原題（1）建立回歸模型，回歸結果如下：Dependent Variable: YMethod: Least SquaresDate: 11/26/10 Time: 19:47Sample: 1970 1994Included observations: 25Coef

10、ficientStd. Errort-StatisticProb.X1.5297120.05097630.008460.0000C-68.1602615.26513-4.4650960.0002R-squared0.975095Mean dependent var388.0000Adjusted R-squared0.974012S.D. dependent var43.33397S.E. of regression6.985763Akaike info criterion6.802244Sum squared resid1122.420Schwarz criterion6.899754Log

11、 likelihood-83.02805Hannan-Quinn criter.6.829289F-statistic900.5078Durbin-Watson stat0.348288Prob(F-statistic)0.000000給定n=25，,在的顯著水平下，查DW統計表可知，。模型中，所以可以判斷模型中存在正自相關。（2）對模型的修正1）采廣義差分法修正自相關：使用普通最小二乘法估計的估計值，得由上式可知=0.873772，對原模型進行廣義差分，得到廣義差分方程：回歸結果如下：Dependent Variable: Y-0.873772*Y(-1)Method: Least Squa

12、resDate: 11/26/10 Time: 20:04Sample (adjusted): 1971 1994Included observations: 24 after adjustmentsCoefficientStd. Errort-StatisticProb.X-0.873772*X(-1)1.2520330.1877946.6670590.0000C3.1980657.7907390.4104960.6854R-squared0.668922Mean dependent var54.86397Adjusted R-squared0.653873S.D. dependent va

13、r6.671848S.E. of regression3.925217Akaike info criterion5.652375Sum squared resid338.9612Schwarz criterion5.750547Log likelihood-65.82850Hannan-Quinn criter.5.678420F-statistic44.44968Durbin-Watson stat1.322343Prob(F-statistic)0.000001給定n=24，,在的顯著水平下，查DW統計表可知，。模型中，DW值落在了無法判斷的區域。所以修正后的模型為：2）一階差分法對模型進

14、行一階差分，回歸結果如下：Dependent Variable: Y-Y(-1)Method: Least SquaresDate: 11/26/10 Time: 20:37Sample (adjusted): 1971 1994Included observations: 24 after adjustmentsCoefficientStd. Errort-StatisticProb.X-X(-1)1.3333330.13142210.145430.0000R-squared0.652682Mean dependent var6.208333Adjusted R-squared0.65268

15、2S.D. dependent var6.678839S.E. of regression3.936084Akaike info criterion5.619023Sum squared resid356.3333Schwarz criterion5.668109Log likelihood-66.42828Hannan-Quinn criter.5.632046Durbin-Watson stat1.591830給定n=24，,在的顯著水平下，查DW統計表可知，。模型中，因此模型已不存在自相關。3）德賓兩步法 建立輔助回歸方程，回歸結果如下：Dependent Variable: YMeth

16、od: Least SquaresDate: 11/26/10 Time: 20:43Sample (adjusted): 1971 1994Included observations: 24 after adjustmentsCoefficientStd. Errort-StatisticProb.C-7.63364112.84334-0.5943660.5589X1.1726220.1885276.2199190.0000X(-1)-1.0062720.254581-3.9526660.0008Y(-1)0.8962550.1239097.2331720.0000R-squared0.99

17、2083Mean dependent var391.6667Adjusted R-squared0.990896S.D. dependent var40.10927S.E. of regression3.827019Akaike info criterion5.673061Sum squared resid292.9215Schwarz criterion5.869403Log likelihood-64.07673Hannan-Quinn criter.5.725151F-statistic835.4552Durbin-Watson stat1.369050Prob(F-statistic)

18、0.000000 把的回歸系數看做的一個估計值，之后進行廣義差分，回歸模型為：回歸結果如下：Dependent Variable: Y-0.896255*Y(-1)Method: Least SquaresDate: 11/26/10 Time: 20:47Sample (adjusted): 1971 1994Included observations: 24 after adjustmentsCoefficientStd. Errort-StatisticProb.X-0.896255*X(-1)1.2010310.1893056.3444250.0000C4.6528996.595502

19、0.7054660.4879R-squared0.646596Mean dependent var46.19771Adjusted R-squared0.630532S.D. dependent var6.352384S.E. of regression3.861224Akaike info criterion5.619501Sum squared resid327.9990Schwarz criterion5.717672Log likelihood-65.43401Hannan-Quinn criter.5.645545F-statistic40.25173Durbin-Watson st

20、at1.305817Prob(F-statistic)0.000002給定n=24，,在的顯著水平下，查DW統計表可知，。模型中，DW值落在了無法判斷的區域。2調換X和Y之后（1）建立回歸模型，回歸結果如下：Dependent Variable: YMethod: Least SquaresDate: 12/04/10 Time: 11:21Sample: 1970 1994Included observations: 25CoefficientStd. Errort-StatisticProb.X0.6374370.02124230.008460.0000C50.874548.2910586

21、.1360730.0000R-squared0.975095Mean dependent var298.2000Adjusted R-squared0.974012S.D. dependent var27.97320S.E. of regression4.509491Akaike info criterion5.926864Sum squared resid467.7167Schwarz criterion6.024374Log likelihood-72.08580Hannan-Quinn criter.5.953909F-statistic900.5078Durbin-Watson sta

22、t0.352762Prob(F-statistic)0.000000給定n=25，,在的顯著水平下，查DW統計表可知，。模型中，所以可以判斷模型中存在正自相關。（2）對模型的修正1）采廣義差分法修正自相關：使用普通最小二乘法估計的估計值，得由上式可知=0.850961，對原模型進行廣義差分，得到廣義差分方程：回歸結果如下：Dependent Variable: Y-0.850961*Y(-1)Method: Least SquaresDate: 12/04/10 Time: 11:17Sample (adjusted): 1971 1994Included observations: 24 a

23、fter adjustmentsCoefficientStd. Errort-StatisticProb.X-0.850961*X(-1)0.5351250.0747937.1547960.0000C13.973344.7894362.9175330.0080R-squared0.699417Mean dependent var48.03762Adjusted R-squared0.685754S.D. dependent var4.550930S.E. of regression2.551144Akaike info criterion4.790616Sum squared resid143

24、.1833Schwarz criterion4.888787Log likelihood-55.48739Hannan-Quinn criter.4.816661F-statistic51.19110Durbin-Watson stat2.377660Prob(F-statistic)0.000000給定n=24，,在的顯著水平下，查DW統計表可知，。模型中，因此可以判斷模型不存在自相關。所以修正后的模型為：6.5參考解答：（1）建立回歸模型，回歸結果如下：Dependent Variable: LOG(Y)Method: Least SquaresDate: 05/07/10 Time: 0

25、0:17Sample: 1980 2000Included observations: 21CoefficientStd. Errort-StatisticProb.C2.1710410.2410259.0075290.0000LOG(X)0.9510900.03889724.451230.0000R-squared0.969199Mean dependent var8.039307Adjusted R-squared0.967578S.D. dependent var0.565486S.E. of regression0.101822Akaike info criterion-1.64078

26、5Sum squared resid0.196987Schwarz criterion-1.541307Log likelihood19.22825Hannan-Quinn criter.-1.619196F-statistic597.8626Durbin-Watson stat1.159788Prob(F-statistic)0.000000給定n=21，,在的顯著水平下，查DW統計表可知，。模型中，所以可以判斷模型中存在正自相關。（2）采用廣義差分法修正自相關：使用普通最小二乘法估計的估計值，得由上式可知=0.400234，對原模型進行廣義差分，得到廣義差分方程：回歸結果如下：Depend

27、ent Variable: LOG(Y)-0.400234*LOG(Y(-1)Method: Least SquaresDate: 05/07/10 Time: 00:21Sample (adjusted): 1981 2000Included observations: 20 after adjustmentsCoefficientStd. Errort-StatisticProb.C1.4770950.2256366.5463720.0000LOG(X)-0.400234*LOG(X(-1)0.9059890.05976715.158710.0000R-squared0.927357Mean dependent var4.882162Adjusted R-squared0.923321S.D. dependent var0.344052S.E. of regression0.095271Akaike inf