精编第五章异方差例题资料

1、26410590131122107406503431588898950779819 1222 1702 1578 1654 1400 1829 2200 2017 2105 1600 2250 2420 2570 1720 1900 2100 2800第五章习题答案演示一、数据如下：（表 5.1 ）Y X87779210 9954 10508 10979 11912 12747 13499 14269 15522 16730 17663 18575 19635 21163 22880 24127 25604 26500 26760 28300 27430 29560 28150 32100 3

2、2500 35250 33500 36000 36200 28200、数据输入EVIEW歎件，注意输入过程中要定义 e2足上EV j.t i q it &r i q c kvs iwTy “弋wO“F 号n p 色 o斗w 亍电*wth.15业a i于Depe ndent Variable: Yi_ 口 xcnrs-辰 iWWTTTILTEUDT- i c”结果如下：（表5.2 ）quick 采单下 estimate equatio nhz zTLOnn 5 i nrin 0-54 .nriQ WGOQ-OO i ogizuuQ11 1 H 1 IJU H77 47 I in 1*0? DOI

3、遇2旳口 15；52Z!-OO 1G7ODJUQII Z ldldl I JIJ1 FEFi7Fi Fl厂Iririm iOS OOQO go.nOQDO 131 .OOOO 12 Ji. DODO1 UULU 抽口冃nnim扫口曰 4B1 8 5SS.OOOO 9D.DQDO mmu UULU 77=? nnmNANAMAKEAMANLANANANAMLA.IXILAKIAMethod: Least SquaresDate: 04/13/08 Time: 16:01Sample: 1 31In cluded observati ons: 31VariableCoefficie ntStd.

4、Errort-StatisticProb.C-700.4110116.6679-6.0034580.0000X0.0878310.00482718.195750.0000R-squared0.919464Mean depe ndent var1266.452Adjusted R-squared0.916686S.D.dependent var846.7570S.E. of regressi on244.4088Akaike info criteri on13.89790Sum squared resid1732334.Schwarz criteri on13.99042Log likeliho

5、od-213.4175F-statistic331.0852Durb in -Watson stat1.089829Prob(F-statistic)0.000000最小二乘估计结果如下Estimati on Comma nd:LS Y CXEstimati on Equati on:Y = C(1) + C(2) *XSubstituted Coefficie nts:Y = -700.4109607 + 0.08783115594*X三、检验模型的异方差:（一）图形法1、EViews软件操作。由路径： Quick/Qstimate Equation，进入 Equation Specific

6、ation 窗口，键入“ y cx”，确认并“ ok”，得样本回归估计结果，见表5.2。（1）生成残差平方序列。在得到表5.2估计结果后，回到以下界面：灯EiesEile Eli t Qbjcls iew Erocs GuLck Oti ons JLiindopr tllpmVoEkfile 1MTITLED回凶Yi uif I 户丁0 | iGbj.GliaJ 詆化 | Ldbd+Q | Eh. | Fti;rh|gnT |Range*: 1 31Sample 1 31回QSi 2 0焰胡回XFilter: * Default Eq: UnlrtledDb点击“ procs ” 下的“ ge

7、n erate series”菜单，输入公式“ e2=(resid)A2Q.DJ 4C1 EPi 外FraexE.ick QEtieTvs 也 awkw Htlp口口.t I Par u. | DL电工 |j _ SbiFW | LeSi | 乡七oar |Range: 1 31 Filteir: * DBfaull Eq: UntrtlBd SampIlR： 1 引Generrale Series by EquatidelSaritiieil 31H5U UUJUe2已经生成，即残差序列生成）Eil Edi w jwlp! ? TTHTT Tl.EZDVulcTa 1 = rrHTXTT-H

8、UJ l)|Tm |X |FT7V t 4w | fir | Ob J * 4 ti I11霑矿*.書*1迪占 t+/* 11I Tit IobsX” 1E21i3777.0002G4.OOOO37440.73Z曰刃.!1O5.DOOO12.34SO9I399G4 !90 口口7032.4I0506. 1 31 .00000 375.65S1 曰产曰.122.DOOO20132.0111912 1Q7.DOQQS7Q41 .G77I2747. OD4QG.OOOOH73.52221#曰曰.5O3.DOOO316.05391牛142G9 401 口口14047 QG1OI5522. 588.00

9、0056I 0.645111673O.OO曰曰曰.口H663H.5IO1217GG3 950 QOQO9EI1Q 7SS1310575.DD77.0000231 20.04(2)在该界面下：单击“ views ”菜单下的“ multple graphs ”下的“ scatter ” ,操作如下:仪 ETiewig.j It 邸i L 打即亡Ltyvi-cli: gtL eo.i fajidw 护lp（3）显示结杲如下（图5.1 ）:30002000 Y1000 _0 J|010000200003000040000400000 300000 -E 200000 -100000 . L / . .

10、 p0 010000200003000040000X2（4）从图5.3分析可知：大致看出残差平方e随Xi的变动呈增大的趋势，因此，模型很可能存在异方差。但是否确实存在异方差还应通过更进一步的检验。（二） Goldfeld-Quanadt 检验1、EViews软件操作。（1）对变量取值排序（按递增或递减）。在Procs菜单里选Sort Series命令，出现排 序对话框，如果以递增型排序，选 Ascenging，如果以递减型排序，则应选 Descending，键 入X,点ok。本例选递增型排序，这时变量 Y与X将以X按递增型排序。EH* E析 qgi* r鈿鼎tinfc* Urlpn=31，删除

11、中间1/4的观(2)构造子样本区间，建立回归模型。在本例中，样本容量测值，即大约9个观测值，余下部分平分得两个样本区间：1 11和21 31,它们的样本个数均是11个，即n n2 =11。由路径： Quick/Qstimate Equation，进入 Equation Specification窗口，键入“ y cx”，确认并ok”，得样本回归估计结果，(注意：sampled 11 )(表 5.3)Depe ndent Variable: YMethod: Least SquaresDate: 04/13/08 Time: 22:26Sample: 1 11In cluded observat

12、i ons: 11VariableCoefficie ntStd. Errort-StatisticProb.C-744.6351195.4108-3.8106140.0041X0.0882580.0157055.6196190.0003R-squared0.778216Mean depe ndent var331.3636Adjusted R-squared0.753574S.D.dependent var260.8157S.E. of regressi on129.4724Akaike info criteri on12.72778Sum squared resid150867.9Schw

13、arz criteri on12.80012Log likelihood-68.00278F-statistic31.58011Durb in -Watson stat1.142088Prob(F-statistic)0.000326Estimati on Comma nd:LS Y CXEstimati on Equati on:Y = C(1) + C(2)*XSubstituted Coefficie nts:Y = -744.6350676 + 0.08825777732*X由路径： Quick/QstimateEquation，进入 Equation Specification窗口，

14、键入“ y cx”，确认并ok”，得样本回归估计结果，（注意：sample:21 31 ）输出结果如下（表5.4）Depe ndent Variable: YMethod: Least SquaresDate: 04/14/08 Time: 10:27Sample: 21 31In cluded observati ons: 11VariableCoefficie ntStd. Errort-StatisticProb.C666.3811911.25850.7312760.4832X0.0457790.0278981.6409710.1352R-squared0.230295Mean depe

15、 ndent var2152.909Adjusted R-squared0.144772S.D.dependent var354.4462S.E. of regressi on327.7867Akaike info criteri on14.58557Sum squared resid966997.0Schwarz criteri on14.65791Log likelihood-78.22063F-statistic2.692786Durb in -Watson stat2.743586Prob(F-statistic)0.135222Estimati on Comma nd:LS Y C

16、XEstimati on Equati on:Y = C(1) + C(2)*XSubstituted Coefficie nts:Y = 666.3810693 + 0.04577902024*X（3）求F统计量值。基于表 5.3和表5.4中残差平方和的数据，即Sumsquared resid的值。由表5.3计算得到的残差平方和为 、e1i2 =150867.9，由表5.4计算得到的残差平、.2方和为7 e1i966997.0，根据Goldfeld-Quanadt检验，F统计量为e2i2966997F =26.41z e1i150867.9(5.1)（4）判断。在=0.05下，式（5.1 ）

17、中分子、分母的自由度均为11,查F分布表得临界值为 F(0.05)(11 -2,11-2) =3.18，因为 F =6.41F(q5)(11 - 2,11 - 2) = 3.18，所以拒绝原假设，表明模型确实存在异方差。（三）White检验由表 5.2 估计结果，按路径 view/residual tests/white heteroskedasticity (no crossterms or cross terms ），进入 White检验。根据 White检验中辅助函数的构造，最后一项为变量的交叉乘积项，因为本例为一元函数，故无交叉乘积项，因此应选no cross terms ，则辅助函数

18、为匚2 = ： 0 丄引 Xtgx； - vt(5.2)经估计出现 White检验结果，见表5.5。y 2从表5.5可以看出，nR2 =9.1026，由White检验知，在，=0.05下，查 分布表,2得临界值计算的0.05（2） =5.9915 （在（5.2 ）式中只有两项含有解释变量，故自由度为2），比较2统计量与临界值，因为 nR2 =9.10265.9915，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。表5.5White Heteroskedasticity Test:F-statistic5.819690Probability0.007699Obs*R-squared9.10

19、2584Probability0.010554Test Equati on:Depe ndent Variable: RESIDA2Method: Least SquaresDate: 04/14/08Time: 11:02Sample: 1 31In eluded observati ons: 31VariableCoefficie ntStd. Errort-StatisticProb.C19975.9882774.930.2413290.8111X-2.1986328.094419-0.2716230.7879XA20.0001460.0001760.8300460.4135R-squa

20、red0.293632Mean depe ndent var55881.73Adjusted R-squared0.243177S.D.dependent var77875.67S.E. of regressi on67748.39Akaike info criteri on25.17675Sum squared resid1.29E+11Schwarz criteri on25.31553Log likelihood-387.2397F-statistic5.819690Durb in -Watson stat2.580140Prob(F-statistic)0.007699四、异方差性的修

21、正（一）加权最小二乘法（ WLS在运用WLS法估计过程中，我们分别选用了权数wit XtXt。数的生成过程如下，由图 5.4，的主菜单中点击quick ”下的Estimation Equation ”键, 输入公式：Y C X,同时，点击“option ”键，在菜单中“weight ”后面的空白处输入 “ 1/X” ,Equatkn 吕 pedhc 出 ion:E srrTtiJcn SettingsM泌LS 屮畀|汎$网毎屮1)14 占百Ftocii-rt-E点击该键, 输入权重ad PDL I Bins. OR ATieLil Equation冋-HatiOEi;Tarktil: IJRT

22、1TLED1巴广 FYgiJgtJmT l Fyini |耳4增 |电 | E/ti.i/i：枣 |1旺切*11$1|E quahm 吕 pecdichlicfYLSartdTSLSOpiw:tfl*Hwk.edskiConsul eiM* WsHwyWdliepEn-dert vfiiiatie Id: 叔PPL l#ira$.QR#M权重：可赋予 不同形式， 目标是消除 异方差I 划制 Wfi RIOCiKlPtS迪敬卄审刹tor% jCOdMns-才 lkciasl MfeinuEiiYiAiuri $tyiohyhdd|lLS Least 5q 匹自州詔唸打5LE LunavdAM M

23、h 4F5MA Wgjffc-S I5u|s| bqu-riivu !Wi-!U Log likelihood Durtiri-WihOni tilF面仅给出用权数 Wit的结果。Depe ndent Variable: YMethod: Least SquaresDate: 04/25/08Time: 22:28Sample: 1 31In cluded observati ons: 31Weight ing series: 1/XVariableCoefficie ntStd. Errort-StatisticProb.C-742.468471.91567-10.324150.0000X0

24、.0897510.00434720.646960.0000Weighted StatisticsR-squared0.786117Mean depe ndent var903.0766Adjusted R-squared0.778742S.D.dependent var406.6195S.E. of regressi on191.2661Akaike info criteri on13.40755Sum squared resid1060899.Schwarz criteri on13.50006Log likelihood-205.8170F-statistic426.2970Durb in -Watson stat1.081175Prob(F-statistic)0.000000Un weighted StatisticsR-squared0.919023Mean depe ndent var1266.452Adjusted R-square