1、 實 驗 報 告課程名稱： 計量經(jīng)濟(jì)學(xué) 實驗項目： 實驗五 異方差模型的 檢驗和處理 實驗類型：綜合性 設(shè)計性 驗證性R專業(yè)班別： 13國貿(mào)10 姓 名： 陳鳳妍 學(xué) 號： 413011003 實驗課室： 厚德A404 指導(dǎo)教師： 石立 實驗日期： 廣東商學(xué)院華商學(xué)院教務(wù)處 制 一、實驗項目訓(xùn)練方案小組合作：是 否R小組成員：無實驗?zāi)康模赫莆债惙讲钅Ｐ偷臋z驗和處理方法實驗場地及儀器、設(shè)備和材料實驗室：普通配置的計算機(jī)，Eviews軟件及常用辦公軟件。實驗訓(xùn)練內(nèi)容（包括實驗原理和操作步驟）：【實驗原理】異方差的檢驗：圖形檢驗法、Goldfeld-Quanadt檢驗法、White檢驗法、Glejs

2、er檢驗法；異方差的處理：模型變換法、加權(quán)最小二乘法(WLS)。【實驗步驟】本實驗考慮三個模型：【1】廣東省財政支出CZ對財政收入CS的回歸模型；（數(shù)據(jù)見附表1：附表1-廣東省數(shù)據(jù)）【2】廣東省固定資產(chǎn)折舊ZJ對國內(nèi)生產(chǎn)總值GDPS和時間T的二元回歸模型；（數(shù)據(jù)見附表1：附表1-廣東省數(shù)據(jù)）【3】廣東省各市城鎮(zhèn)居民消費支出Y對人均收入X的回歸模型。（數(shù)據(jù)見附表2：附表2-廣東省2005年數(shù)據(jù)）（一）異方差的檢驗1.圖形檢驗法分別用相關(guān)分析圖和殘差散點圖檢驗?zāi)Ｐ汀?】、模型【2】和模型【3】是否存在異方差。注：相關(guān)分析圖是作因變量對自變量的散點圖（亦可作模型殘差對自變量的散點圖）；殘差散點圖是作

3、殘差的平方對自變量的散點圖。模型【2】中作圖取自變量為GDPS來作圖。模型【1】相關(guān)分析圖 殘差散點圖模型【2】相關(guān)分析圖 殘差散點圖模型【3】相關(guān)分析圖 殘差散點圖【思考】相關(guān)分析圖和殘差散點圖的不同點是什么？*在模型【2】中，自變量有兩個，有無其他處理方法？嘗試做出來。（請對得到的圖表進(jìn)行處理，以上在一頁內(nèi)）2.Goldfeld-Quanadt檢驗法用Goldfeld-Quanadt檢驗法檢驗?zāi)Ｐ汀?】是否存在異方差。注：Goldfeld-Quanadt檢驗法的步驟為：排序：刪除觀察值中間的約1/4的，并將剩下的數(shù)據(jù)分為兩個部分。構(gòu)造F統(tǒng)計量：分別對上述兩個部分的觀察值求回歸模型，由此得到

4、的兩個部分的殘差平方為和。為較大的殘差平方和，為較小的殘差平方和。算統(tǒng)計量。判斷：給定顯著性水平，查F分布表得臨界值。如果，則認(rèn)為模型中的隨機(jī)誤差存在異方差。（詳見課本135頁）將實驗中重要的結(jié)果摘錄下來，附在本頁。obsX1Y117021.944632.6927220.4399999999996317.0337299.256350.3848241.2099999999996463.36999999999958842.8400000000016757.0269214.67294.9379867.367476.649999999999810097.27669.84910908.368113.64

5、00000000011011944.088296.431112229.179505.661215762.7712651.951317680.114323.661418287.2414468.241518907.7314485.611621015.0318550.561722881.821188.841828665.2521767.78Dependent Variable: Y1Method: Least SquaresDate: 05/27/16 Time: 12:49Sample: 1 7Included observations: 7CoefficientStd. Errort-Stati

6、sticProb.  X10.6949620.2103463.3038990.0214C741.06461747.4610.4240810.6891R-squared0.685846    Mean dependent var6470.296Adjusted R-squared0.623015    S.D. dependent var930.0264S.E. of regression571.0279    Akaike info criterion15

7、.76771Sum squared resid1630364.    Schwarz criterion15.75226Log likelihood-53.18698    Hannan-Quinn criter.15.57670F-statistic10.91575    Durbin-Watson stat1.749751Prob(F-statistic)0.021383Dependent Variable: Y1Method: Least SquaresDate: 05

8、/27/16 Time: 12:50Sample: 12 18Included observations: 7CoefficientStd. Errort-StatisticProb.  X10.7914140.1472585.3743270.0030C586.59523068.7330.1911520.8559R-squared0.852435    Mean dependent var16776.66Adjusted R-squared0.822922    S.D. dependent v

9、ar3677.261S.E. of regression1547.415    Akaike info criterion17.76151Sum squared resid11972459    Schwarz criterion17.74606Log likelihood-60.16530    Hannan-Quinn criter.17.57050F-statistic28.88339    Durbin-Watson stat1

10、.957878Prob(F-statistic)0.003004（請對得到的圖表進(jìn)行處理，以上在一頁內(nèi)）3.White檢驗法分別用White檢驗法檢驗?zāi)Ｐ汀?】、模型【2】和模型【3】是否存在異方差。Eviews操作：先做模型，選view/Residual Tests/White Heteroskedasticity (no cross terms/cross terms)。摘錄主要結(jié)果附在本頁內(nèi)。模型【1】Heteroskedasticity Test: WhiteF-statistic4.940866    Prob. F(2,25)0.0156Ob

11、s*R-squared7.932189    Prob. Chi-Square(2)0.0189Scaled explained SS14.57723    Prob. Chi-Square(2)0.0007Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 05/27/16 Time: 13:19Sample: 1978 2005Included observations: 28CoefficientStd. Errort-Stat

12、isticProb.  C-879.85131125.376-0.7818290.4417CS12.937204.6513282.7813980.0101CS2-0.0066200.002964-2.2335610.0347R-squared0.283292    Mean dependent var1940.891Adjusted R-squared0.225956    S.D. dependent var4080.739S.E. of regression3590.225 

13、60;  Akaike info criterion19.31077Sum squared resid3.22E+08    Schwarz criterion19.45351Log likelihood-267.3508    Hannan-Quinn criter.19.35441F-statistic4.940866    Durbin-Watson stat2.144291Prob(F-statistic)0.015552從模型結(jié)果看出，nR

14、78;=7.932189，由White檢驗知，在=0.05下，查x2分布表，得臨界值X²0.05(2)=5.99147，比較計算的統(tǒng)計量與臨界值，nR²=7.932189> X²0.05(2)=5.99147 ,所以拒絕原假設(shè)， 不拒絕備擇假設(shè)，表明模型存在異方差。模型【2】Heteroskedasticity Test: WhiteF-statistic1.993171    Prob. F(5,22)0.1195Obs*R-squared8.729438   

15、60;Prob. Chi-Square(5)0.1204Scaled explained SS14.67857    Prob. Chi-Square(5)0.0118Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 05/27/16 Time: 13:31Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.  C1837.8986243.7010

16、.2943600.7712GDPS-3.3950935.407361-0.6278650.5366GDPS2-9.08E-050.000185-0.4895370.6293GDPS*T0.1603000.3151760.5086040.6161T-491.56141982.891-0.2479010.8065T249.08543152.98750.3208460.7514R-squared0.311766    Mean dependent var3461.910Adjusted R-squared0.155349   &#

17、160;S.D. dependent var7240.935S.E. of regression6654.775    Akaike info criterion20.63147Sum squared resid9.74E+08    Schwarz criterion20.91694Log likelihood-282.8405    Hannan-Quinn criter.20.71874F-statistic1.993171    

18、;Durbin-Watson stat1.971537Prob(F-statistic)0.119510從模型結(jié)果看出，nR²=8.729438，由White檢驗知，在=0.05下，查x2分布表，得臨界值X²0.05(2)=5.99147，比較計算的統(tǒng)計量與臨界值，nR²=8.729438> X²0.05(2)=5.99147 ,所以拒絕原假設(shè)， 不拒絕備擇假設(shè)，表明模型存在異方差。模型【3】Heteroskedasticity Test: WhiteF-statistic7.670826   &#

19、160;Prob. F(2,15)0.0051Obs*R-squared9.101341    Prob. Chi-Square(2)0.0106Scaled explained SS14.09286    Prob. Chi-Square(2)0.0009Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 05/27/16 Time: 13:32Sample: 1 18Included observations: 18Coeffic

20、ientStd. Errort-StatisticProb.  C1865425.2810916.0.6636360.5170X-354.7917388.1454-0.9140690.3751X20.0188100.0116861.6095970.1283R-squared0.505630    Mean dependent var1232693.Adjusted R-squared0.439714    S.D. dependent var2511199.S.E. of regression1

21、879689.    Akaike info criterion31.88212Sum squared resid5.30E+13    Schwarz criterion32.03052Log likelihood-283.9391    Hannan-Quinn criter.31.90258F-statistic7.670826    Durbin-Watson stat2.010913Prob(F-statistic)0.005

22、074從模型結(jié)果看出，nR²=9.101341，由White檢驗知，在=0.05下，查x2分布表，得臨界值X²0.05(2)=5.99147，比較計算的統(tǒng)計量與臨界值，nR²=9.101341> X²0.05(2)=5.99147 ,所以拒絕原假設(shè)， 不拒絕備擇假設(shè)，表明模型存在異方差。（請對得到的圖表進(jìn)行處理，以上在一頁內(nèi)）4.Glejser檢驗法用Glejser檢驗法檢驗?zāi)Ｐ汀?】是否存在異方差。分別用殘差的絕對值對自變量的一次項、二次項，開根號項和倒數(shù)項作回歸。檢驗異方差是否存在，并選定異方差的最優(yōu)形式。摘錄主要結(jié)果附在本

23、頁內(nèi)。(1)對CS回歸Dependent Variable: ABS(RESID)Method: Least SquaresDate: 05/27/16 Time: 14:10Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.  CS0.0292360.0122792.3809470.0249C14.159918.2594921.7143800.0984R-squared0.179006    Mean dependent va

24、r27.30288Adjusted R-squared0.147429    S.D. dependent var35.20964S.E. of regression32.51074    Akaike info criterion9.869767Sum squared resid27480.66    Schwarz criterion9.964925Log likelihood-136.1767    Hannan-Quinn cr

25、iter.9.898858F-statistic5.668911    Durbin-Watson stat1.339465Prob(F-statistic)0.024881(2)去掉常數(shù)項再進(jìn)行回歸Dependent Variable: E1Method: Least SquaresDate: 05/27/16 Time: 14:11Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.  CS0.0433040.

26、0094564.5794730.0001R-squared0.086198    Mean dependent var27.30288Adjusted R-squared0.086198    S.D. dependent var35.20964S.E. of regression33.65794    Akaike info criterion9.905436Sum squared resid30587.14    Schwarz c

27、riterion9.953015Log likelihood-137.6761    Hannan-Quinn criter.9.919981Durbin-Watson stat1.209310(3)對回歸Dependent Variable: E1Method: Least SquaresDate: 05/27/16 Time: 14:19Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.  CS21.11E-

28、058.36E-061.3222070.1976C22.302367.5752862.9440940.0067R-squared0.063003    Mean dependent var27.30288Adjusted R-squared0.026965    S.D. dependent var35.20964S.E. of regression34.73168    Akaike info criterion10.00193Sum squared resid31363.

29、53    Schwarz criterion10.09709Log likelihood-138.0270    Hannan-Quinn criter.10.03102F-statistic1.748231    Durbin-Watson stat1.203183Prob(F-statistic)0.197614 (4)對回歸Dependent Variable: E1Method: Least SquaresDate: 05/27/16 Time: 14:20Samp

30、le: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.  CS(1/2)1.5372330.2690365.7138480.0000R-squared0.265081    Mean dependent var27.30288Adjusted R-squared0.265081    S.D. dependent var35.20964S.E. of regression30.1843

31、2    Akaike info criterion9.687583Sum squared resid24599.52    Schwarz criterion9.735162Log likelihood-134.6262    Hannan-Quinn criter.9.702128Durbin-Watson stat1.471849(5)對作回歸Dependent Variable: E1Method: Least SquaresDate: 05/27/16 Time:

32、14:28Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.  CS(-1)-2029.779607.7392-3.3398840.0025C46.202298.0122115.7664840.0000R-squared0.300226    Mean dependent var27.30288Adjusted R-squared0.273311    S.D. depen

33、dent var35.20964S.E. of regression30.01483    Akaike info criterion9.710009Sum squared resid23423.14    Schwarz criterion9.805167Log likelihood-133.9401    Hannan-Quinn criter.9.739100F-statistic11.15483    Durbin-Watson

34、 stat1.566457Prob(F-statistic)0.002542從四個回歸的結(jié)果看，第二個不顯著，其他三個顯著，比較這三個回歸，還是選擇第三個，方程為ABS(RESID)=1.53723330222*CS(1/2)即異方差的形式為：²=（1.537233*（CS(1/2)）²=2.36085CS也即異方差的形式為：²=²CS就把這個形式確定為異方差的形式。 對ZJ與GDPS和T回歸的Glejser檢驗可以類似進(jìn)行檢驗，消費支出與可支配收入回歸的Glejser檢驗可以類似進(jìn)行檢驗。 通過前面實驗的異方差模型的檢驗，發(fā)現(xiàn)根據(jù)廣東數(shù)據(jù)CZ對CS的回

35、歸，ZJ對GDPS和T的回歸，消費支出與可支配收入回歸都存在異方差，現(xiàn)在分別對它們進(jìn)行處理。加權(quán)最小二乘法已經(jīng)成為處理異方差模型的標(biāo)準(zhǔn)方法，再Eviews中使用WLS來消除異方差，關(guān)鍵是權(quán)數(shù)的選取。 （請對得到的圖表進(jìn)行處理，以上在一頁內(nèi)）（二）異方差的處理1.模型【1】中CZ對CS回歸異方差的處理已知CZ對CS回歸異方差的形式為：，選取權(quán)數(shù)，使用加權(quán)最小二乘法處理異方差。并檢驗處理異方差之后模型是否仍存在異方差，若仍然存在異方差，請繼續(xù)處理異方差。摘錄主要結(jié)果附在本頁內(nèi)。Dependent Variable: CZMethod: Least SquaresDate: 05/27/16 Tim

36、e: 14:32Sample: 1978 2005Included observations: 28Weighting series: 1/(CS(1/2)CoefficientStd. Errort-StatisticProb.  CS1.2756770.01940665.736280.0000C-21.243654.264097-4.9819800.0000Weighted StatisticsR-squared0.994019    Mean dependent var254.4606Adjusted R-squared0.99

37、3789    S.D. dependent var189.1988S.E. of regression22.86683    Akaike info criterion9.166001Sum squared resid13595.19    Schwarz criterion9.261159Log likelihood-126.3240    Hannan-Quinn criter.9.195092F-statistic4321.25

38、9    Durbin-Watson stat1.550317Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.995276    Mean dependent var552.2429Adjusted R-squared0.995095    S.D. dependent var653.1881S.E. of regression45.74872    Sum square

39、d resid54416.57Durbin-Watson stat1.545575回歸方程為 CZ=1.2756769685*CS-21.2436468305它與存在異方差的如下方程估計有所不同。 CZ=1.27887365026*-CS-22.6807299594至于經(jīng)過加權(quán)最小二乘法估計的殘差項是否存在異方差，同樣可以用本實驗的異方差模型的檢驗去檢驗，但是若在eviews中使用wls命令估計的序列resed不能用倆檢驗，因為產(chǎn)生的序列resid是非加權(quán)方式的殘差。要想檢驗只能自己進(jìn)行同方差變換，然后回歸以后再檢驗了。進(jìn)行同方差行變換，然后回歸實際上就是CZ/(CS(1/2)對1/(CS(1

40、/2)和CS/(CS(1/2)回歸，結(jié)果如下：Dependent Variable: CZ/(CS(1/2)Method: Least SquaresDate: 05/27/16 Time: 14:35Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.  1/(CS(1/2)-21.243654.264097-4.9819800.0000CS/(CS(1/2)1.2756770.01940665.736280.0000R-squared0.985934 &#

41、160;  Mean dependent var21.13688Adjusted R-squared0.985393    S.D. dependent var15.71588S.E. of regression1.899444    Akaike info criterion4.189748Sum squared resid93.80503    Schwarz criterion4.284906Log likelihood-56.65647 

42、   Hannan-Quinn criter.4.218839Durbin-Watson stat1.550317觀察其殘差趨勢圖還是存在異方差，再改為CZ/CS對1/CS和回歸，如果如下:Dependent Variable: CZ/CSMethod: Least SquaresDate: 05/27/16 Time: 14:44Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.  1/CS-19.828602.064540-9.604

43、3680.0000C1.2625010.02721846.384560.0000R-squared0.780115    Mean dependent var1.077876Adjusted R-squared0.771658    S.D. dependent var0.213378S.E. of regression0.101963    Akaike info criterion-1.659667Sum squared resid0.270307  

44、  Schwarz criterion-1.564510Log likelihood25.23534    Hannan-Quinn criter.-1.630577F-statistic92.24388    Durbin-Watson stat1.613436Prob(F-statistic)0.000000觀察其殘差趨勢圖應(yīng)該不存在異方差了，其方程為CZ/CS=-19.8286033657*1/CS+1.26250140483變換為原方程為CZ=-19.8286033657+1.26250

45、140483*CS（請對得到的圖表進(jìn)行處理，以上在兩頁內(nèi)）2.模型【2】中ZJ對GDPS和T回歸異方差的處理已知ZJ對GDPS和T回歸異方差的形式為：，選取權(quán)數(shù)，使用加權(quán)最小二乘法處理異方差。并檢驗處理異方差之后模型是否仍存在異方差，若仍然存在異方差，請繼續(xù)處理異方差。摘錄主要結(jié)果附在本頁內(nèi)。Dependent Variable: ZJMethod: Least SquaresDate: 05/27/16 Time: 14:47Sample: 1978 2005Included observations: 28Weighting series: 1/(GDPS(3/8)CoefficientS

46、td. Errort-StatisticProb.  GDPS0.1669950.00256565.100680.0000T-4.3536850.881296-4.9400930.0000Weighted StatisticsR-squared0.997009    Mean dependent var418.9342Adjusted R-squared0.996894    S.D. dependent var382.1762S.E. of regression29.59878 &#

47、160;  Akaike info criterion9.682092Sum squared resid22778.28    Schwarz criterion9.777250Log likelihood-133.5493    Hannan-Quinn criter.9.711183Durbin-Watson stat0.668750Unweighted StatisticsR-squared0.996289    Mean dependent var

48、846.0661Adjusted R-squared0.996146    S.D. dependent var1014.824S.E. of regression63.00261    Sum squared resid103202.6Durbin-Watson stat0.754208回歸方程為它與存在異方差時的如下方程估計也有所不同。進(jìn)行同方差性變換，然后回歸實際上就是ZJ/(GDPS(8/3)對GDPS/(GDPS(8/3)和T/(GDPS(8/3)回歸，結(jié)果如下：Dependent Variable: Z

49、J/(GDPS(3/8)Method: Least SquaresDate: 05/27/16 Time: 14:49Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.  GDPS/(GDPS(3/8)0.1669950.00256565.100680.0000T/(GDPS(3/8)-4.3536850.881296-4.9400930.0000R-squared0.994224    Mean dependent var27

50、.59529Adjusted R-squared0.994002    S.D. dependent var25.17403S.E. of regression1.949678    Akaike info criterion4.241955Sum squared resid98.83235    Schwarz criterion4.337112Log likelihood-57.38737    Hannan-Quinn crite

51、r.4.271045Durbin-Watson stat0.668750觀測其殘差趨勢圖可能還存在異方差，再改為ZJ/GDPS對C和T/GDPS回歸，結(jié)果如下：Dependent Variable: ZJ/GDPSMethod: Least SquaresDate: 05/27/16 Time: 14:51Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.  T/GDPS-3.7265040.399838-9.3200440.0000C0.1619500.003461

52、46.793580.0000R-squared0.769633    Mean dependent var0.135596Adjusted R-squared0.760772    S.D. dependent var0.021590S.E. of regression0.010560    Akaike info criterion-6.194729Sum squared resid0.002899    Schwarz criterion-6.099572Log likelihood88.72621    Hannan-Quinn criter.-6.165638F-statistic86.86322    Durbin-Watson stat0.439676Prob(F-statistic)0.000000觀測其殘差趨勢圖應(yīng)該不存在異方差了，其方程為變換為原方程（請對得到的圖表進(jìn)行處理，以上在兩頁內(nèi)）3.模型【3】中消費支出Y對可支配收入X回歸異方差的處理已知Y對X回歸異方差的形式為：，選取權(quán)數(shù)，使用加權(quán)