異方差檢驗的eviews操作

第四章異方差性例4.1。4一、參數(shù)估計進入Eviews軟件包，確定時間范圍，編輯輸入數(shù)據(jù)；選擇估計方程菜單：(1)在Workfile對話框中，由路徑：Quick/EstimateEquation，進入EquationSpecification對話框，鍵入“[og(y)clog(x1)log(x2)”，確認ok，得到樣本回歸估計結(jié)果；(2)直接在命令欄里輸入"*log(y)clog(x1)log(x2)”，按Enter，得到樣本回歸估計結(jié)果；⑶在Group的當前窗口，由路徑：Procs/MakeEquation,進入EquationSpecification窗口，鍵入“l(fā)og(y)clog(x1)log(x2)〃，確認ok，得到樣本回歸估計結(jié)果。如表4。1：表4。1□即endentVariable:LOG(Y)Method:LeastSquaresDate:06/11Time:23:60Sample:131Includedobsen/ations:31Variable CoefficientStd.Errort-StatisticProb.03.2660681.041591 3.1356530.0040LOG(X1)0.1502140.108536 1.3839750.1773LOG(X2)0.4774530.051595 9.2536530.0000R-squared0779878Meandependentvar7.928613AdjustedR-squared0764155S.D.dependentvar0.355760S.E.ofregression0.172766Akaikeinfacriterion-0.581995Sumsquaredresid0.835744Schwarzcriterior-0.443222Loglikelihood12.02092F-statistic49.60117Durbin-Watsonstat1780981Prob(F-statistic)□.□00000R-sq陽樹；樣本成定系匏Mesn var因變JI的均值A(chǔ)djusted 哨整后的樣本決定慕數(shù)S.D,d^penjentwt:因職量的標傕差SErt^ressufii:回歸痣鹿溪菠Akaikeinfocniaicn:赤池信息置WC)Sumsquaredresid：淺差平方和Schwarz 魘瓦麹信息量(SC)1;0￡版5血時：對數(shù)似檢比F-s前旅;F檢理的統(tǒng)計量Durbtn-Wa^cnscat:DW統(tǒng)t僵Prob(F-SLatistic):相伴概一軋圖4.1估計結(jié)果為：LnY=3.266+0.1502LI1X1+0.4775LI1X2(3。>14)(1。38) (9。25)R2=0.7798 D.W。=1。78F=49。60 RSS=0.8357括號內(nèi)為t統(tǒng)計量值。二、檢驗?zāi)Ｐ偷漠惙讲睿ㄒ唬﹫D形法（1）生成殘差平方序列。①在Workfile的對話框中，由路徑：Procs/GenerateSeries，進入GenerateSeriesbyEquation對話框，鍵入“e2=resid^2”，生成殘差平方項序列e2；②直接在命令欄里輸入“genre2=resid^2”，按Enter，得到殘差平方項序列e2.（2）繪制散點圖。直接在命令框里輸入“scatlog（x2）e2",按Enter，可得散點圖4。2。選擇變量名log（x2）與e2（注意選擇變量的順序，先選的變量將在圖形中表示橫軸，后選的變量表示縱軸），再按路徑view/graph/scatter/simplescatter,可得散點圖4。2。由路徑quick/graph進入serieslist窗口，輸入“l(fā)og（x2）e2”，確認并ok,再在彈出的graph窗口把linegraph換成scatterdiagram，再點ok,可得散點圖4.2。圖4.2由圖4.2可以看出，殘差平方項e2對解釋變量log（X2）的散點圖主要分布圖形中的下三角部分，大致看出殘差平方項e2隨log（X2）的變動呈增大的趨勢，因此，模型很可能存在異方差。但是否確實存在異方差還應(yīng)通過更進一步的檢驗.（二）Goldfeld-Quanadt檢驗（1） 對變量取值排序（按遞增或遞減）。在Workfile窗口中，由路徑：Procs/SortSeries進入sortworkfileseries對話框，鍵入“X2”，如果以遞增型排序，選Ascending，如果以遞減型排序，則應(yīng)選Descending，點ok。本例選遞增型排序，選Ascendingo直接在命令欄里輸入“sortx2"（默認為升序），再按Enter。（2） 構(gòu)造子樣本區(qū)間，建立回歸模型.在本例中，樣本容量n=31，刪除中間1/4的觀測值，即大約7個觀測值，余下部分平分得兩個樣本區(qū)間：1—12和20-31，它們的樣本個數(shù)均是12個。在Sample菜單里，把sample值改為“112”再用OLS方法進行第一個子樣本回歸估計，估計結(jié)果如表4.2。表4。2DependentVariable:LOG(Y)Method:LeastSquaresDate:05/13/11Time:03:00Sample:112Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.C3.1412081.1223582.7987570.0208LOG(X1)0.3983850.0787916.0662340.0007LOG(X2)0.2347510.1097472.1390090.0611R-squared0739693Meandeperdentvar7.700632AdjustedR-sqjared0.681847S.D.dependentvar0.166674S.E.ofregression0.088316Akaikeinfocriterion-1.803481Sumsquaredresid0.070197Schwarzcriterion-1.682265Leglikelihood13.820B9F-statistic127B726Durbin-Watsonstat1.298449Prob(F-statistic)0.002343同樣地，在Sample菜單里，把sample值改為“2031”再用OLS方法進行第二個子樣本回歸估計，估計結(jié)果如表4.3。表4。3DependentVariable:LOG(Y)Method:LeastSquaresDate:0M3/11Time:03:04Sample:2031Includedobservations:12VariableCoefficientStd.Errort-StatisticProL.C3.9936441.3040542.1197000.0631LOG(X1)-0.1137660.159962-0.7112050.4950LOG(X2)0.6201680.1116545.5543000.0004R-squared0.876931Meandependentvar8.239746AdjustedR-squared0.849582S.D.dependentvar0.375812S.E.ofregression0.145754Akaikeinfocriterion■0.801478Sumsquaredresid0.191197Schwaricriterion■0.680251Loglikelihood7.808868F-statistic32.06485Durbin-Watsonstat2.565362Prob(F-statistic)0.000080(3)求F統(tǒng)計量值?；诒?。2和表4.3中殘差平方和RSS的數(shù)據(jù)，即Sumsquaredresid的值，得到RSS1=0。0702和RSS2=0。1912,根據(jù)Goldfeld-Quanadt檢驗，F(xiàn)統(tǒng)計量為:F=RSS2/RSS1=0。1912/0。0702=2。73。(4)判斷。在5%與10%的顯著性水平下，查F分布表得：自由度為(9,9)的F分布的臨界值分別為F005=3.18與F010=2。44。因為F=2.73<F005(9,9)=3.18，因此5%顯著性水平下不拒絕兩組子樣方差相同的假設(shè)，但F=2。73>F010(9,9)=2。44,因此10%顯著性水平下拒絕兩組子樣方差相同的假設(shè)，即存在異方差。(三)White檢驗①由表4。1的估計結(jié)果，按路徑view/residualtests/whiteheteroskedasticity(crossterms)，進入White檢驗，其中crossterms表示有交叉乘積項。得到表4.4的結(jié)果.表4.4WhiteHeteroskedasticitvTest:F-statistic9.833740Probability0.000027Obs*R-squared20.55085Probability0.000985TestEquation:DependentVariable:RESIDEMethod:LeastSquaresDate:05/13/11Time:01:13Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.C10.243205.4745221.B710B20.0731LOG(X1)-2.3290701.116442-2.0B61530.0473[LOG而)程0.1491140.05B1072.5661950.0167(LOG(X1)f(LOG(X2))0.0193330.0412650.4605070.6435LOG(X2)-0.4573070.454020-1.0072380.3235(LOGpb))^20.0211010.0133571.5796940.1267R-squared0.662931Meandependentvar0.026959AdjustedR-sqjared0.595517S.D.dependentvar0.042129S.E.ofregression0.026794Akaikeinfocriterian-4.229312Sumsquaredresid0.017940Schwarzcriterion-3.951?66Loglikelihood71.55434F-statistic9.833740Durbin-Watsonstat1.462377Prob(F-statistic}0.000027輔助回歸結(jié)果為：ez=10.2+-233LnXl-0.46LnX2+O.lS(LnXl)2+0.02(LnX2)3+0.02LnXlLnX2(1.87) (-2.09) (-1。01) (2.56) (1.58) (0.47)R2=0.6629由表4。4結(jié)果得到：懷特統(tǒng)計量nR2=31X0。6629=20.55，查X2分布表得到在5%的顯著性水平下，自由度為5的X2分布的臨界值為X2005=11。07,因為nR2=20.55>x20.05=11.07,所以拒絕同方差的原假設(shè)。②由表4。1的估計結(jié)果，按路徑view/residualtests/whiteheteroskedasticity(nocrossterms)，進入White檢驗，其中nocrossterms表示無交叉乘積項。得

到表4.5的結(jié)果。表4.5WhiteHeteroskedasticitvTest:F-statistic12.61602Prababilit/0.000008Obs*R-squared20.45911Prababilit/0.000405TestEquation:DependentVariable:RESIDEMethod:LeastSquaresDate:05/13/11Time:01:32Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProL.C7.7632751.375324 5.6446900.0000LQG的)-1.8511230.446727-4.1437430.0003(LOG[X1))-^20.1261600.030767 4.1005120.0004LOG(X2)-0.2581660.157160-1.6426970.11250.0172140.010311 1.6695110.1070R-squared0.659971Meandependentvar0.026969AdjustedR-sqjared0.607659S.D.dependentvar0.042129S.E.ofregression0.026309Akaikeinfocriterian-4.205007Sumsquaredresid0.018106Schwarzcriterion-4.053798Loglikelihood71.41884F-statistic12.61602Durbin-Watsonstat1.481064Prob(F-statistic)0.000008去掉交叉項后的輔助回歸結(jié)果為：決=7.763-l.BSlLnXl-0258LnX2+0.126(LnXl)2+O.O17(LnX2)2(5.64) (—4.14)(-1。64)(4。10)(1.67)R2=0.6599有懷特統(tǒng)計量nR2=31X0。6599=20。46,因此，在5%的顯著性水平下，仍是拒絕同方差這一原假設(shè)，表明模型存在異方差.三、異方差性的修正(一)加權(quán)最小二乘法(WLS)生成權(quán)數(shù)。按路徑：Procs/GenerateSeries，進入GenerateSeriesbyEquation對話框，鍵入“w=1/sqr(exp(93.20-25。981*log(x2)+1.701*(log(x2))A2))”或者直接在命令欄輸入“genrw=1/sqr(exp(93.20-25.981*log(x2)+1。701*(log(x2))A2))"生成權(quán)數(shù)w。加權(quán)最小二乘法估計(WLS)。在表4。1的結(jié)果中，由路徑：Procs/Specify/Estimate進入EquationSpecification對話框，點擊Options按鈕，在EstimationOptions對話框的weighted前面打勾并在下面輸入欄處輸入w,如圖4.3，連續(xù)兩次確認OK后，得到表4。6的估計結(jié)果：EstirrazionGptcniLSandTSLS0ptions:HeteroskedasticitAJ

ConsistentCovariance+LSandTSLS0ptions:HeteroskedasticitAJ

ConsistentCovariance+WhiteNewejJ-WeslrWeightedLS/TSLS(unavailabl已withARMA)Weight:回Iterativeprocedures:M朋Iterations:|100Convergence:10.001ARMAoptions:Startingcoefficientvalues|OLS/TSLS>BackcastMAterms)OK J^Cancel圖4。3

表4。5DependeritVariable:LOG(Y)Method:LeastSquaresDate:05/13/11Time:01:59Sample:131Includedobservations;31Weightingseries;WVariableCoefficientStd.Errort-StatisticProb.C2.33963207245953.2288820.0032LOGQ<1)0.3170970.0833773.8031770.0007LOGCX2)0.4290980.0446309.6145170.0000WeightedStatisticsR-sqjared0.998375Meandependentwar7.8S3773AdjustedR-squared0.998259S.D.dependentwar2.766804S.E.ofregr&ssiori0.115025Akaikeirfocriterion-1.396661Sumsquaredresid0.370464Schwarzcriterion-1.2667S8Loglikelihood24.63119F-statistic8602.1S3Durbin-Watsonstat1.716616Prob(F-statistic)0.000000加權(quán)最小二乘法估計(WLS)結(jié)果為：LnY=2.34+0,317LnXl+0.429LnX2(3.23) (3.80) (9.61)R2=0.9984 D。W。=1.72F=8602.18RSS=0.3705可以看出運用加權(quán)最小二乘法消除異方差性后，LnX1參數(shù)的t檢驗有了顯著的改進,這表明即使在1%顯著性水平下，都不能拒絕從事農(nóng)業(yè)生產(chǎn)帶來的純收入對農(nóng)戶人均消費支出有著顯著影響的假設(shè)。雖然LnX1的參數(shù)值有了較大程度的提高，但仍沒有LnX2的參數(shù)估計值大,說明其他來源的純收入確實比來自農(nóng)業(yè)經(jīng)營的純收入對農(nóng)戶人均消費支出的影響更大一些。

檢驗加權(quán)回歸模型的異方差性.在命令欄中直接輸入“l(fā)sw*log(Y)ww*log(X1)w*log(X2)”，按回車鍵，輸出結(jié)果如表4。6：表4。6DependentVariable:W^LOGfY)Method:LeastSquaresDate;05/13/11Time;02;21Sample;131Incljdedobservations:31VariableCoefficientStd.Errort-StatisticProb.W2.3396320.724595 3.2288820.0032W"LOGQ<1)0.3170970.083377 3.8031770.0007WLOGCX2)0.4290980.044630 9.6145170.0000R-squared0.998376Meandependentvar112.9506AdjustedR-squared0.998269S.D.dependentvar39.49666S.E.ofregression1.647967Akaikeinfocriterion3.928728Sumsquaredresid76.04228Schwarzcriterion4.067501Loglikelihood-57.89528F-statistic8602.183Durbin-Watsorstat1.716616Prob(F-statistic]0.000000得到的加權(quán)回歸模型的OLS回歸結(jié)果：wLnY=2.34w+0.317wLnXl+0,429wLnX2對該模型進行懷特檢驗，得到無交叉乘積項的回歸結(jié)果如表4.7所示:表4。7WhiteHeteroskedasticitvTest:F=：statistic1.15G30GProbability0.235156Ob