實驗五異方差模型的檢驗

1、實驗報告課程名稱：計量經(jīng)濟學(xué)實驗項目：實驗五異方差模型的檢驗和處理實驗類型：綜合性口設(shè)計性口 驗證性專業(yè)班別：12國姓 名：學(xué) 號：412實驗課室：厚德樓 A404/11/14指導(dǎo)教師：實驗日期：2015年5月28日廣東商學(xué)院華商學(xué)院教務(wù)處制I、實驗項目訓(xùn)練方案;,小組合作：是口否小組成員：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，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、Glejser檢 驗法；異方差的處理：模型變換

2、法、加權(quán)最小二乘法 （WLS）?！緦嶒灢襟E】本實驗考慮三個模型：【1】廣東省財政支出CZ寸財政收入CS勺回歸模型；（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寸人均收入X的回歸模型。（數(shù)據(jù)見附表2: 附表2-廣東省200成數(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。二' ' y注：相關(guān)分析圖是作應(yīng)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

3、是作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？ 一 一 、 、一 . 一 、 一 - 在模型【2】中，自變量有兩個，有無其他處理方法？嘗試做出來。（請對得到的圖表講行處理，以上在一頁內(nèi) ）2.Goldfeld-Quanadt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

4、部分的觀察值求回歸 v e2 . cc模型，由此得到的兩個部分的殘差平方為 1i和工最。£ e2為較大的殘差平方和,2£最為較小的殘差平方和。算統(tǒng)計量5*=三粵5（色£_匕3_2。判斷：% e2i22）給定顯著性水平a =0.05,查F分布表得臨界值F（n,）（nq 3）。如果 （i尤|二IF*F（nq （nq （口），則認(rèn)為模型中的隨機誤差存在異方差。（詳見課本135頁）（ k, k）22將實驗中重要的結(jié)果摘錄下來，附在本頁。obsXY17021.9427220.446317.0337299.256463.3746350.3858842.846757.02692

5、14.67294.9379867.367669.84810097.27476.65910908.368113.641011944.088296.43111229.179505.661215762.7712651.951317680.114485.611418287.2414468.241518907.7314323.661621015.0318550.561722881.821767.781828665.2521188.84Dependent Variable: YMethod: Least SquaresDate: 06/07/15Time: 11:18Sample: 1 7Included

6、 observations: 7VariableCoefficientStd. Errort-StatisticProb.?X0.7230770.2183863.3110030.0212C536.88741814.2540.2959270.7792R-squared0.686771?Mean dependent var6497.894Adjusted R-squared0.624125?S.D. dependent var966.9988S.E. of regression592.8541 ?Akaike info criterion15.84273Sum squared resid17573

7、80. ?Schwarz criterion15.82728Log likelihood-53.44956 ?Hannan-Quinn criter.15.65172F-statistic10.96274 ?Durbin-Watson stat1.761325Prob(F-statistic)0.021217Dependent Variable: YMethod: Least SquaresDate: 06/07/15 Time: 11:20Sample: 12 18Included observations: 7VariableCoefficientStd. Errort-Statistic

8、Prob.?X0.7592910.1778984.2681250.0080C1243.7433707.2380.3354900.7509R-squared0.784640?Mean dependent var16776.66Adjusted R-squared0.741567?S.D. dependent var3677.261S.E. of regression1869.382?Akaike info criterion18.13956Sum squared resid?Schwarz criterion18.12411Log likelihood-61.48846?Hannan-Quinn

9、 criter.17.94855F-statistic18.21689?Durbin-Watson stat2.037081Prob(F-statistic)0.007953有上圖可知£ e2 , Z e2i =1757380?F=?£ e2/£武 在 =0.05下，上式中分子、分母的自由度均為5,查F分布表得臨界值F0.05 (5,5) =5.05,因為F=?F0.05 (5,5) =5.05,所以拒接- -"1、. 1. jIX 原假設(shè)，說明模型存在異方差。？(請對得到的圖表進行處理，以上在一頁內(nèi))3.White檢驗法分別用White檢驗法檢驗?zāi)Ｐ汀?/p>

10、1】、模型【2】和模型【3】是否存在異方差。Eviewsft作：先做模型，選 view/Residual Tests/ Heteroskedasticity Tests/White/ 選cross terms摘錄主要結(jié)果附在本頁內(nèi)。模型【1】Heteroskedasticity Test: White4.F-statistic40866?Prob. F(2,25)0.0156Obs*R-squared7.932189?Prob. Chi-Square(2)0.0189Scaled explained SS14.57723?Prob. Chi-Square(2)0.0007Test Equati

11、on:Dependent Variable: RESIDA2Method: Least SquaresDate: 06/07/15 Time: 12:44Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?C-879.85131125.376-0.7818290.4417CS12.937204.6513282.7813980.0101CSA2-0.0066200.002964-2.2335610.0347R-squared0.283292?Mean dependent v

12、ar1940.891Adjusted R-squared0.225956?S.D. dependent var4080.739S.E. of regression3590.225?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模型【2】1H

13、eteroskedasticity Test: White: x 1F-statistic1.993171?Prob. F(5,22)0.1195Obs*R-squared8.729438?Prob. Chi-Square(5)0.1204Scaled explained SS14.67857?Prob. Chi-Square(5)0.0118Test Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 06/07/15 Time: 12:47Sample: 1978 2005Included observations:

14、 28VariableCoefficientStd. Errort-StatisticProb.?C1837.8986243.7010.2943600.7712GDPS-3.3950935.407361-0.6278650.5366GDPSA2-9.08E-050.000185-0.4895370.6293GDPS*T0.1603000.3151760.5086040.6161T-491.56141982.891-0.2479010.8065TA249.08543152.98750.3208460.7514R-squared0.311766?Mean dependent var3461.910

15、Adjusted R-squared0.155349?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-statisticProb(F-statistic)1.9931710.119510?Durbin-Watson stat1.971537模型【3】Heteroskedas

16、ticity Test: WhiteF-statistic7.670826?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: RESIDA2Method: Least SquaresDate: 06/07/15 Time: 12:51Sample: 1 18Included observations: 18VariableCoefficientSt

17、d. Errort-StatisticProb.?C1865425.2810916.0.6636360.5170X-354.7917388.1454-0.9140690.3751XA20.0188100.0116861.6095970.1283R-squared0.505630?Mean dependent var1232693.Adjusted R-squared0.439714?S.D. dependent var2511199.S.E. of regression1879689.?Akaike info criterion31.88212Sum squared resid5.30E+13

18、?Schwarz criterion32.03052Log likelihood-283.9391?Hannan-Quinn criter.31.90258F-statistic7.670826?Durbin-Watson stat2.010913Prob(F-statistic)0.005074（請對得到的圖表進行處理，以上在一頁內(nèi) ）4.Glejser檢驗法用Glejse檢驗法檢驗?zāi)Ｐ汀?】是否存在異方差。2分別用殘差的絕對值對自變量的一次項cs、二次項CS；,開根號項VC§和倒數(shù)項1fCSi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)果附在本頁內(nèi)。一、一次項C

19、Si回歸Dependent Variable: E1Method: Least SquaresDate: 06/07/15 Time: 13:17Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?CS0.0292360.0122792.3809470.0249C14.159918.2594921.7143800.0984R-squared0.179006?Mean dependent var27.30288Adjusted R-squared0.147429?S.D.

20、dependent var35.20964S.E. of regression32.51074?Akaike info criterion9.869767Sum squared resid27480.66?Schwarz criterion9.964925Log likelihood-136.1767?Hannan-Quinn criter.9.898858F-statistic5.668911?Durbin-Watson stat1.339465Prob(F-statistic)0.024881二、去掉常數(shù)項再回歸？Dependent Variable: E1Method: Least Sq

21、uaresDate: 06/07/15 Time: 13:22Sample: 1978 2005Included observations: 28 1 VariableCoefficientStd. Errort-StatisticProb.?CS0.0433040.0094564.5794730.0001R-squared0.086198?Mean dependent var27.30288Adjusted R-squared0.086198?S.D. dependent var35.20964S.E. of regression33.65794?Akaike info criterion9

22、.905436Sum squared resid30587.14?Schwarz criterion9.953015Log likelihood-137.6761?Hannan-Quinn criter.9.919981Durbin-Watson stat1.209310三、二次項CS2回歸Dependent Variable: E1Method: Least SquaresDate: 06/07/15 Time: 13:19Sample: 1978 2005 'j 1;Included observations: 28VariableCoefficientStd. Errort-St

23、atisticProb.?CSA21.11E-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 resid31363.53?Schwarz criterion10.09709Log likelihood-138

24、.0270?Hannan-Quinn criter.10.03102F-statistic1.748231?Durbin-Watson stat1.203183Prob(F-statistic)0.197614四、開根號項qCST回歸Dependent Variable: E1Method: Least SquaresDate: 06/07/15 Time: 13:24Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?CSA(1/2)1.5372330.2690365.

25、7138480.0000R-squared0.265081?Mean dependent var27.30288Adjusted R-squared0.265081?S.D. dependent var35.20964S.E. of regression30.18432?Akaike info criterion9.687583Sum squared resid24599.52?Schwarz criterion9.735162Log likelihood-134.6262?Hannan-Quinn criter.9.702128Durbin-Watson stat1.471849一五、傕J數(shù)

26、項1/CSi作回歸Dependent Variable: E1i 3,！Method: Least Squaresc 1I,< -Date: 06/07/15 Time:13:26Sample: 1978 2005Included observations: 2811VariableCoefficientStd. Errort-StatisticProb.?CSA(-1)-2029.779607.7392-3.3398840.0025c46.202298.0122115.7664840.0000R-squared0.300226?Mean dependent var27.30288Adj

27、usted R-squared0.273311?S.D. dependent 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 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

28、個顯著，比較這三個回歸，還是選 擇第三個，方程為即異方差的形式為：6 2=(1.537233* (CSA(1/2) ) 2=2.36085csi也即異方差的形式為：CTi 2= (T 2CS就把這個形式確定為異方差的形式。對ZJ與GDPS口 T回歸的Glejser檢驗可以類似進行檢驗，消費支出與可支配收 入回3的Glejser檢驗可以類似進行檢驗。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的回歸，ZJ對GDP制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 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

29、權(quán)數(shù)的選取。（請對得到的圖表進行處理，以上在一頁內(nèi)）（二）異方差的處理I .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：52 =D2CSi ,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II / / 廣；異方差。摘錄主要結(jié)果附在本頁內(nèi)。-J 1|'1Dependent Variable: CZ .= - -Method: Least Squaresi 1 IDate: 06/07/15 Time: 13:32Sample: 1978 2005Included observations: 28

30、Weighting series: 1/(CSA(1/2)-nJ.f,1.1- 11 ,VariableCoefficientStd. Errort-StatisticProb.?CS1.2756770.01940665.736280.0000C-21.243654.264097-4.9819800.0000.T.| 1Weighted StatisticsR-squared0.994019 ?Mean dependent var254.4606Adjusted R-squared0.993789 ?S.D. dependent var189.1988S.E. of regression22.

31、86683 ?Akaike info criterion19.166001Sum squared resid13595.19 ?Schwarz criterion |9.261159Log likelihood-126.3240 ?Hannan-Quinn criter.9.195092F-statistic4321.259 ?Durbin-Watson stat1.550317Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.995276 ?Mean dependent var552.2429Adjusted R-squared

32、0.995095 ?S.D. dependent var653.1881S.E. of regression45.74872 ?Sum squared resid54416.57Durbin-Watson stat1.545575回歸方程為它與存在異方差的如下方程估計有所不同。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行同方差變換，然 后回歸以后再檢驗了。進行同方差行變換，然后回歸實際上就是CZ/(CSA(1/

33、2)對1/(CSA(1/2)和CS/(CSA(1/2)回歸，結(jié)果如下：Dependent Variable: CZ/(CSA(1/2)Method: Least SquaresDate: 06/07/15 Time: 13:39Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?1/(CSA(1/2)-21.243654.264097-4.9819800.0000CS/(CSA(1/2)1.2756770.01940665.736280.0000R-squared0.98

34、5934?Mean dependent var-r21.13688Adjusted R-squared0.985393?S.D. dependent var15.71588 U |S.E. of regression1.899444?Akaike info criterion4.189748Sum squared resid93.80503?Schwarz criterion4.284906Log likelihoodDurbin-Watson stat-56.656471.550317?Hannan-Quinn criter. -21 j 74.218839觀察其殘差趨勢圖 -一1還是存在異

35、方差，再改為CZ/CS對1/CS和回歸，如果如下Dependent Variable: CZ/CSMethod: Least SquaresDate: 06/07/15 Time: 13:42Sample: 1978 2005-、-； JIncluded observations: 28Variable:CoefficientStd. Errort-StatisticProb.?1/CS-19.828602.064540-9.6043680.0000C1.2625010.02721846.384560.0000R-squared0.780115?Mean dependent var1.0778

36、76Adjusted R-squared0.771658?S.D. dependent var0.213378S.E. of regression0.101963?Akaike info criterion-1.659667Sum squared resid0.270307?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(謂對得到

37、的圖表講行處理，以上在兩貞內(nèi) )2 .模型【2】中ZJ對GDP7口T回歸異方差的處理C3已知ZJ對GDPS和T回歸異方差的形式為：52 =a2(GDPSi，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: 06/07/15 Time: 13:46Sample: 1978 2005Included observations: 28Weighting series: 1/(GDPSA(3/8)Variabl

38、eCoefficientStd. Errort-StatisticProb.?GDPS0.1669950.00256565.100680.0000T-4.3536850.881296-4.9400930.0000.門I i 1WeightedStatisticsIIR-squared0.997009?Mean dependent var418.9342Adjusted R-squared0.996894?S.D. dependent var382.1762S.E. of regression29.59878?Akaike info criterion9.682092Sum squared re

39、sid22778.28?Schwarz criterion9.777250Log likelihood-133.5493?Hannan-Quinn criter.9.711183Durbin-Watson stat0.668750 Unweighted StatisticsR-squaredAdjusted R-squaredS.E. of regression Durbin-Watson stat0.9962890.99614663.002611 10.754208?Mean dependent var?S.D. dependent var?Sum squared resid846.0661

40、1014.824103202.6,、.r 、， . z . ir、 .、廣.匕與仔仕異力差時的如卜力桂值訂也切所/、問。進行同方差性變換，然后回歸實際上就是ZJ/(GDPSA(8/3)對GDPS/(GDPSA(8/3)和T/(GDPSA(8/3)回歸，結(jié)果如下：Dependent Variable: ZJ/(GDPSA(3/8)Method: Least SquaresDate: 06/07/15 Time: 13:50Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?

41、GDPS/(GDPSA(3/8)0.1669950.00256565.100680.0000T/(GDPSA(3/8)-4.3536850.881296-4.9400930.0000R-squared0.994224?Mean dependent var27.59529Adjusted R-squared0.994002?S.D. dependent var25.17403S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat1.949678 ?Akaike info criterion98.83235 ?S

42、chwarz criterion4.2419554.3371124.271045-57.387370.668750?Hannan-Quinn criter.觀測具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: 06/07/15 Time:13:52Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?jf /1 1 / J-J nC0

43、.1619500.00346146.793580.0000T/GDPS-3.7265040.399838-9.3200440.0000 IR-squared0.769633?Mean dependent varh M0.135596I- ) / * /Adjusted R-squared0.760772?S.D. dependent var0.021590S.E. of regression0.010560?Akaike info criterion-6.194729Sum squared resid0.002899?Schwarz criterion-6.099572Log likeliho

44、od88.72621?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 二" ： 二4已知Y對X回歸異方差的形式為：52=<r2(Xi F,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

45、內(nèi)。Dependent Variable: YMethod: Least SquaresDate: 06/07/15 Time: 13:56Sample: 1 18Included observations: 18Weighting series: 1/XA(2/3)VariableCoefficientStd. Errort-StatisticProb.?X0.7951570.01725246.090120.0000Weighted StatisticsR-squared0.954867 ?Mean dependent var9599.510Adjusted R-squared0.95486

46、7 ?S.D. dependent var1867.615S.E. of regression895.7229 ?Akaike info criterion16.48709Sum squared resid?Schwarz criterion16.53656Log likelihood-147.3838 ?Hannan-Quinn criter.16.49391Durbin-Watson stat1.472431Unweighted StatisticsR-squared0.952547 ?Mean dependent var10906.35Adjusted R-squared0.952547

47、 ?S.D. dependent var5381.587S.E. of regression1172.315 ?Sum squared residDurbin-Watson stat1.419465r" 它與存在異方差時如下方程估計明顯不同進行同方差性變換，然后回歸實際上就是Y/(XA(2/3)和X/(XA(2/3)回歸，結(jié)果如Dependent Variable: Y/(XA(2/3) -h *Method: Least Squares IDate: 06/07/15 Time: 13:59Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.?1/(XA(2/3)-495.5562520.4173-0.9522280.3551X/(XA(2/3)0.8337080.04402618.936730.0000R-squared0.782313?Mean dependent var18.56257Adjusted R-squared0.768707?S.D. depend