實(shí)驗(yàn)五異方差模型的檢驗(yàn)

Documentserialnumber【UU89WT-UU98YT-UU8CB-UUUT-UUT108】Documentserialnumber【UU89WT-UU98YT-UU8CB-UUUT-UUT108】實(shí)驗(yàn)五異方差模型的檢驗(yàn)實(shí)驗(yàn)報(bào)告課程名稱：計(jì)量經(jīng)濟(jì)學(xué)實(shí)驗(yàn)項(xiàng)目：實(shí)驗(yàn)五異方差模型的檢驗(yàn)和處理實(shí)驗(yàn)類型：綜合性□設(shè)計(jì)性□驗(yàn)證性專業(yè)班別：12國姓名：學(xué)號(hào)：412實(shí)驗(yàn)課室：厚德樓A404指導(dǎo)教師：實(shí)驗(yàn)日期：2015年5月28日廣東商學(xué)院華商學(xué)院教務(wù)處制一、實(shí)驗(yàn)項(xiàng)目訓(xùn)練方案小組合作：是□否小組成員：無實(shí)驗(yàn)?zāi)康模赫莆债惙讲钅Ｐ偷臋z驗(yàn)和處理方法實(shí)驗(yàn)場(chǎng)地及儀器、設(shè)備和材料實(shí)驗(yàn)室：普通配置的計(jì)算機(jī)，Eviews軟件及常用辦公軟件。實(shí)驗(yàn)訓(xùn)練內(nèi)容（包括實(shí)驗(yàn)原理和操作步驟）：【實(shí)驗(yàn)原理】異方差的檢驗(yàn)：圖形檢驗(yàn)法、Goldfeld-Quanadt檢驗(yàn)法、White檢驗(yàn)法、Glejser檢驗(yàn)法；異方差的處理：模型變換法、加權(quán)最小二乘法(WLS)?！緦?shí)驗(yàn)步驟】本實(shí)驗(yàn)考慮三個(gè)模型：【1】廣東省財(cái)政支出CZ對(duì)財(cái)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(duì)國內(nèi)生產(chǎn)總值GDPS和時(shí)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(fèi)支出Y對(duì)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(yàn)1.圖形檢驗(yàn)法分別用相關(guān)分析圖和殘差散點(diǎn)圖檢驗(yàn)?zāi)Ｐ汀?】、模型【2】和模型【3】是否存在異方差。注：①相關(guān)分析圖是作應(yīng)變量對(duì)自變量的散點(diǎn)圖（亦可作模型殘差對(duì)自變量的散點(diǎn)圖）；②殘差散點(diǎn)圖是作殘差的平方對(duì)自變量的散點(diǎn)圖。③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(diǎn)圖模型【2】相關(guān)分析圖殘差散點(diǎn)圖模型【3】相關(guān)分析圖殘差散點(diǎn)圖【思考】①相關(guān)分析圖和殘差散點(diǎn)圖的不同點(diǎn)是什么②*在模型【2】中，自變量有兩個(gè)，有無其他處理方法嘗試做出來。（請(qǐng)對(duì)得到的圖表進(jìn)行處理，以上在一頁內(nèi)）檢驗(yàn)法用Goldfeld-Quanadt檢驗(yàn)法檢驗(yàn)?zāi)Ｐ汀?】是否存在異方差。注：Goldfeld-Quanadt檢驗(yàn)法的步驟為：①排序：②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(gè)部分。③構(gòu)造F統(tǒng)計(jì)量：分別對(duì)上述兩個(gè)部分的觀察值求回歸模型，由此得到的兩個(gè)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。④算統(tǒng)計(jì)量。⑤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(shí)驗(yàn)中重要的結(jié)果摘錄下來，附在本頁。obsXY12345678910111

12131415161718DependentVariable:YMethod:LeastSquaresDate:06/07/15Time:11:18Sample:17Includedobservations:7VariableCoefficientStd.Errort-StatisticProb.XCR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresid1757380.SchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)DependentVariable:YMethod:LeastSquaresDate:06/07/15Time:11:20Sample:1218Includedobservations:7VariableCoefficientStd.Errort-StatisticProb.XCR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)有上圖可知，=1757380F=/在下，上式中分子、分母的自由度均為5，查F分布表得臨界值（5,5）=，因?yàn)镕=（5,5）=，所以拒接原假設(shè)，說明模型存在異方差。（請(qǐng)對(duì)得到的圖表進(jìn)行處理，以上在一頁內(nèi)）檢驗(yàn)法分別用White檢驗(yàn)法檢驗(yàn)?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/ResidualTests/HeteroskedasticityTests/White/(勾選crossterms)。摘錄主要結(jié)果附在本頁內(nèi)。模型【1】HeteroskedasticityTest:WhiteF-statistic4.

40866Prob.F(2,25)Obs*R-squaredProb.Chi-Square(2)ScaledexplainedSSProb.Chi-Square(2)TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:06/07/15Time:12:44Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.CCSCS^2R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresid+08SchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)模型【2】HeteroskedasticityTest:WhiteF-statisticProb.F(5,22)Obs*R-squaredProb.Chi-Square(5)ScaledexplainedSSProb.Chi-Square(5)TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:06/07/15Time:12:47Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.CGDPSGDPS^2GDPS*TTT^2R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresid+08SchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)模型【3】HeteroskedasticityTest:WhiteF-statisticProb.F(2,15)Obs*R-squaredProb.Chi-Square(2)ScaledexplainedSSProb.Chi-Square(2)TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:06/07/15Time:12:51Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.C1865425.2810916.XX^2R-squaredMeandependentvar1232693.AdjustedR-squared.dependentvar2511199..ofregression1879689.AkaikeinfocriterionSumsquaredresid+13SchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)（請(qǐng)對(duì)得到的圖表進(jìn)行處理，以上在一頁內(nèi)）檢驗(yàn)法用Glejser檢驗(yàn)法檢驗(yàn)?zāi)Ｐ汀?】是否存在異方差。分別用殘差的絕對(duì)值對(duì)自變量的一次項(xiàng)、二次項(xiàng)，開根號(hào)項(xiàng)和倒數(shù)項(xiàng)作回歸。檢驗(yàn)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(xiàng)回歸DependentVariable:E1Method:LeastSquaresDate:06/07/15Time:13:17Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.CSCR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)

二、去掉常數(shù)項(xiàng)再回歸DependentVariable:E1Method:LeastSquaresDate:06/07/15Time:13:22Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.CSR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.Durbin-Watsonstat三、二次項(xiàng)回歸DependentVariable:E1Method:LeastSquaresDate:06/07/15Time:13:19Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.CS^2CR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)四、開根號(hào)項(xiàng)回歸DependentVariable:E1Method:LeastSquaresDate:06/07/15Time:13:24Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.CS^(1/2)R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.Durbin-Watsonstat

五、倒數(shù)項(xiàng)作回歸DependentVariable:E1Method:LeastSquaresDate:06/07/15Time:13:26Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.CS^(-1)CR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)

從四個(gè)回歸的結(jié)果看，第二個(gè)不顯著，其他三個(gè)顯著，比較這三個(gè)回歸，還是選擇第三個(gè)，方程為即異方差的形式為：σ2=（*（CS^(1/2)））2=也即異方差的形式為：σ2=σ2CS就把這個(gè)形式確定為異方差的形式。對(duì)ZJ與GDPS和T回歸的Glejser檢驗(yàn)可以類似進(jìn)行檢驗(yàn)，消費(fèi)支出與可支配收入回歸的Glejser檢驗(yàn)可以類似進(jìn)行檢驗(yàn)。

通過前面實(shí)驗(yàn)的異方差模型的檢驗(yàn)，發(fā)現(xiàn)根據(jù)廣東數(shù)據(jù)CZ對(duì)CS的回歸，ZJ對(duì)GDPS和T的回歸，消費(fèi)支出與可支配收入回歸都存在異方差，現(xiàn)在分別對(duì)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(qǐng)對(duì)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(duì)CS回歸異方差的處理已知CZ對(duì)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(yàn)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(qǐng)繼續(xù)處理異方差。摘錄主要結(jié)果附在本頁內(nèi)。DependentVariable:CZMethod:LeastSquaresDate:06/07/15Time:13:32Sample:19782005Includedobservations:28Weightingseries:1/(CS^(1/2))VariableCoefficientStd.Errort-StatisticProb.CSCWeightedStatisticsR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)UnweightedStatisticsR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionSumsquaredresidDurbin-Watsonstat

回歸方程為它與存在異方差的如下方程估計(jì)有所不同。至于經(jīng)過加權(quán)最小二乘法估計(jì)的殘差項(xiàng)是否存在異方差，同樣可以用本實(shí)驗(yàn)的異方差模型的檢驗(yàn)去檢驗(yàn)，但是若在eviews中使用wls命令估計(jì)的序列resed不能用倆檢驗(yàn)，因?yàn)楫a(chǎn)生的序列resid是非加權(quán)方式的殘差。要想檢驗(yàn)只能自己進(jìn)行同方差變換，然后回歸以后再檢驗(yàn)了。進(jìn)行同方差行變換，然后回歸實(shí)際上就是CZ/(CS^(1/2)對(duì)1/(CS^(1/2))和CS/(CS^(1/2)回歸，結(jié)果如下：DependentVariable:CZ/(CS^(1/2))Method:LeastSquaresDate:06/07/15Time:13:39Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.1/(CS^(1/2))CS/(CS^(1/2))R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.Durbin-Watsonstat

觀察其殘差趨勢(shì)圖還是存在異方差，再改為CZ/CS對(duì)1/CS和回歸，如果如下:DependentVariable:CZ/CSMethod:LeastSquaresDate:06/07/15Time:13:42Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.1/CSCR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)觀察其殘差趨勢(shì)圖（請(qǐng)對(duì)得到的圖表進(jìn)行處理，以上在兩頁內(nèi)）2.模型【2】中ZJ對(duì)GDPS和T回歸異方差的處理已知ZJ對(duì)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(yàn)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(qǐng)繼續(xù)處理異方差。摘錄主要結(jié)果附在本頁內(nèi)。DependentVariable:ZJMethod:LeastSquaresDate:06/07/15Time:13:46Sample:19782005Includedobservations:28Weightingseries:1/(GDPS^(3/8))VariableCoefficientStd.Errort-StatisticProb.GDPSTWeightedStatisticsR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.Durbin-WatsonstatUnweightedStatisticsR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionSumsquaredresidDurbin-Watsonstat它與存在異方差時(shí)的如下方程估計(jì)也有所不同。進(jìn)行同方差性變換，然后回歸實(shí)際上就是ZJ/(GDPS^(8/3))對(duì)GDPS/(GDPS^(8/3))和T/(GDPS^(8/3)回歸，結(jié)果如下：DependentVariable:ZJ/(GDPS^(3/8))Method:LeastSquaresDate:06/07/15Time:13:50Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.GDPS/(GDPS^(3/8))T/(GDPS^(3/8))R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.Durbin-Watsonstat觀測(cè)其殘差趨勢(shì)圖可能還存在異方差，再改為ZJ/GDPS對(duì)C和T/GDPS回歸，結(jié)果如下：DependentVariable:ZJ/GDPSMethod:LeastSquaresDate:06/07/15Time:13:52Sample:19782005Includedobservations:28VariableCoefficientStd.Errort-StatisticProb.CT/GDPSR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.F-statisticDurbin-WatsonstatProb(F-statistic)

觀測(cè)其殘差趨勢(shì)圖應(yīng)該不存在異方差了，其方程為變換為原方程（請(qǐng)對(duì)得到的圖表進(jìn)行處理，以上在兩頁內(nèi)）3.模型【3】中消費(fèi)支出Y對(duì)可支配收入X回歸異方差的處理已知Y對(duì)X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(yàn)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(qǐng)繼續(xù)處理異方差。摘錄主要結(jié)果附在本頁內(nèi)。DependentVariable:YMethod:LeastSquaresDate:06/07/15Time:13:56Sample:118Includedobservations:18Weightingseries:1/X^(2/3)VariableCoefficientStd.Errort-StatisticProb.XWeightedStatisticsR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.Durbin-WatsonstatUnweightedStatisticsR-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionSumsquaredresidDurbin-Watsonstat

它與存在異方差時(shí)如下方程估計(jì)明顯不同進(jìn)行同方差性變換，然后回歸實(shí)際上就是Y/(X^(2/3))和X/(X^(2/3))回歸，結(jié)果如下：DependentVariable:Y/(X^(2/3))Method:LeastSquaresDate:06/07/15Time:13:59Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.1/(X^(2/3))X/(X^(2/3))R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodHannan-Quinncriter.Durbin-Watsonstat觀測(cè)其殘差趨勢(shì)圖雖然不能夠準(zhǔn)確判斷，但大致還是存