序列相關(guān)的檢驗(yàn)和修正

1、序列相關(guān)的檢驗(yàn)及修正例題：中國居民總量消費(fèi)函數(shù) 數(shù)據(jù)：年份GDPCONSCPITAXGDPCXY19783605.61759.146.21519.287802.6：6678.93806.819794092.62011.547.07537.828694.7 17552.14273.419804592.92331.250.62571.709073.3 17943.94605.319815008.82627.951.90629.899650.9 18437.25063.419825590.02902.952.95700.0210557.1 19235.15482.319836216.23231.15

2、4.00775.5911511.5 110075.25983.519847362.73742.055.47947.3513273.3 111565.46746.019859076.74687.460.652040.7914965.711600.87728.6198610508.55302.164.572090.3716274.6 113037.28211.4198712277.46126.169.302140.3617716.3 114627.88840.0198815388.67868.182.302390.4718698.2 115793.69560.3198917311.38812.69

3、7.002727.4017846.7 115034.99085.2199019347.89450.9100.002821.8619347.8 116525.99450.9199122577.410730.6103.422990.1721830.8 118939.510375.7199227565.213000.1110.033296.9125052.4 122056.111815.1199336938.116412.1126.204255.3029269.5 125897.613004.8199450217.421844.2156.655126.8832057.1 128784.213944.

4、6199563216.928369.7183.416038.0434467.5 131175.415467.9199674163.633955.9198.666909.8237331.9 133853.717092.5199781658.536921.5204.218234.0439987.5 135955.418080.2199886531.639229.3202.599262.8042712.7 138140.519363.9199991125.041920.4199.7210682.5845626.4 140277.620989.6200098749.045854.6200.551258

5、1.5149239.1 142965.622864.42001108972.449213.2201.9415301.3853962.8 146385.624370.22002120350.352571.3200.3217636.4560079.0 151274.926243.72003136398.856834.4202.7320017.3167281.0 157407.128034.52004160280.463833.5210.6324165.6876095.7 164622.730306.02005188692.171217.5214.4228778.5488001.2 174579.6

6、33214.02006221170.580120.5217.6534809.72101617.5 |85624.136811.61、建立回歸模型，模型的OLS估計(jì)Y oiXtt（1 ）錄入數(shù)據(jù)打開 EViews6，點(diǎn)"File”“New”“WorkfileDated reuhr Frequency vWorkfile structure typeDate specflcatkonrjrmes (optionalCancel¥orkflie 匚reateIrregular Dated and Panel workfie5 ma/ be made from Unstructur

7、ed workfiles by later specifying date anchor Cither identifier series.選擇 "Dated-regular frequency”，在 Frequency 后選擇 “Annual”，在 Start data后輸入 1978, 在End data后輸入2006，點(diǎn)擊“ ok”。在命令行輸入：DATA X Y，回車 將數(shù)據(jù)復(fù)制粘貼到 Group中的表格中:(2) 估計(jì)回歸方程在命令行輸入命令：LS Y C X,回車或者在主菜單中點(diǎn)" Quick ”“ Estimate Equation ”，在 Specifica

8、tion 中輸入 Y C X，點(diǎn)“確定”。得到如下輸出： Equatiim: KHTirLED Torkfile: XULIEX1&N&. 回岡I View |Proc Object (PrritjName |Free?e Estimate, Forecast stats, ResidDeperdent Variable- vMethod: Least SquaresDale: 06/08J12 Time: 18:13Sample: 1976 200SIncluded observations. 29CoefficientStd. Errorb StatisticProto.C

9、2OQ1.2Q2334 9917S.2427870.0000X0.4375270.00929747.056870.0000R-squared1987955Mean dependentvar1485572Adjusted R-squared19875OQs.d. dependent var9472.09ES.E. of regression1058.650Aka ike info criterion1 6 83335Sum squared resid3025994SSchwarz criterion16.92614Log likelihood242.0908Hannan-Guinn enter1

10、6 8&33SF-statistic2514.537Durbin-Wat sen stat0.2771 32Prob(F-statistic)o.ooocoo寫出估計(jì)結(jié)果:Y? 2091.28 0.4375X(6.243)(47.059)F=2214.537D.W.=0.2772 2R =0.9880R0.9875 2、序列相關(guān)的檢驗(yàn)(1)圖示檢驗(yàn)法作殘差序列的時(shí)序圖：保存殘差虛列：GENR E=RESID作圖：PLOT E從圖上可以看出，模型的最小二乘殘差開始連續(xù)幾期小于0 ,接著連續(xù)幾期都大于這種模式的殘差意味著模型可能存在正的序列相關(guān)性。做&和& 1的關(guān)系圖：SC

11、AT E(-1) E2,400-1,6002,000 _1,600 -1,200800400 -0 -400 -800-1,20002,000-4,000-2,0004,000從上面的散點(diǎn)圖可以看出,et和 1之間可以擬合一個(gè)線性模型:et = et i t且回歸直線的斜率為正(>0)，表明模型存在正的序列相關(guān)性。(2)DW檢驗(yàn)由OLS估計(jì)的結(jié)果可知：D.W.=0.277。查DW分布的臨界值表，k=2 ,n=29時(shí)，dL=1.34，du =1.48，顯然0<0.277<dL，因此模型存在一階正的自相關(guān)。(3) 回歸檢驗(yàn)法擬合模型：&= et1t，并運(yùn)用 OLS估計(jì)模型

12、：LS E E(-1)得到如下結(jié)果: Equation: UhJTTTLED Workfilg： XLL1EXIANG(31MN:Up | 回|viewProc Object pnnthlarnc .FneE；亡| |日timte FQimet statsReidsDepen dent Vari able: EMettiod' Least SquaresDate 11/07/12 Time 2117Sample fadjlisted): 1979 2006Included observaticns: 28 after adjustmentsCoefficientStd. E rro r

13、l-StatsticPre b.Ef-1)0.948 &72Q.1154608.1494910,0000R-squiared0.710391Mean dependentvar4309574Adjusted R-squared0.710391S.D. dependent var1031.932S E. of regr&ssior555.1373Aka ike infb crttarion15.51209Sum squared resid8326797.Schwarz criterion15.55967Log likelihood-216.1693Hannan-Quinn crit

14、er.15.52663口 ur bin AV ats on stat0.576494寫出回歸結(jié)果：?0.949 1(8.148)回歸系數(shù)的t統(tǒng)計(jì)量為8.148,伴隨概率P=0.0000< =0.05,表明原模型存在一階序列相 關(guān)。擬合模型：et= 1et 12 2t，并運(yùn)用OLS估計(jì)模型：LS E E(-1) E(-2)得到如下結(jié)果:Dependent Variable: EMethod: Least SquaresDate: 1W7/12 Time: 21124Samplie (adjusted: 1980 2006Included observations: 27 after adj

15、iistmentsCoefficientStd Errort-StatisticProbE(d1658591015224310J95000,0000E(-2)-0 8643560155255-5 5673450.0000R-squared0854051Me ar dependentvar85.25222Adjusted R-sqjared0.S56B13S.D. dependent var1025.517G.E. of regression385.6098AJcaike info enterion14.31872Sum squared res id3717374,Schwarz criteri

16、on14.91470Log likelihood-19&0527Hannan-Quinn crite r14.84726Durbin-Watson stat2.317512寫出回歸結(jié)果：?1659 10.864 2(10.895)(-5.567)回歸系數(shù)和的t統(tǒng)計(jì)量分別為10.895、-5.567,相應(yīng)的伴隨概率 P=0.0000< =0.05，表明原模型存在二階序列相關(guān)。擬合模型：et= 1%12%23%3t，并運(yùn)用OLS估計(jì)模型：LS E E(-1)E(-2)E(-3)，回車，得到如下結(jié)果:Dependent Variable: EMethod: Least SquaresD

17、ate: 11/07/12 Time:21:36Sample (adjusted: 1381 200SIncludedoDservations: 26 sft&r adjuslmentsCoefficientStd Erort-StatiSticProb.E(-1)1.4353670.20542172795340.0000E(-2)-04741000371327*1 2767720.2144E卜3)*0.2860350.241900-1.1024510.2491R-squared0.867002Mean dependent var126.556 £Adjusted R-squ

18、ared0 855502S D dependentvar1523.787SE of regression389.1710AkaiKfr info crit&rionM074Q8Sum squared resid3403444,Schwarz criterion15.01925Log likelihood-19 O'.3531Hannan-Ouinn criter.14.91588DurbirvWateM stat2.1704-17寫出回歸結(jié)果:% 1.495%i 0.474%2 0.286%3(7.280)(-1.277)( -1.182)回歸系數(shù)的t統(tǒng)計(jì)量為7.280，相應(yīng)的

19、伴隨概率 P1=0.0000< =0.05，表明顯著不為零，但和的t統(tǒng)計(jì)量分別為-1.277、-1.182，相應(yīng)的伴隨概率 P2=0.2144, P3=0.2491，均大于 =0.05， 表明原模型不存在三階序列相關(guān)。綜上，原模型有二階序列相關(guān)。(4) LM檢驗(yàn)首先采用 OLS 估計(jì)模型，在彈出的Equation窗口，點(diǎn) View Residual Tests Serialcorrelation LM Test，彈出下面的對(duì)話框： 點(diǎn)“OK”得到下面的輸出:Sreusch-Godfrey Serial Correlation LU TestF-slatistic Obs* Squared

20、553440123556S6Pr(Jt>. F(2,25)ProD. ChkSquare(2)0.00000.0000Test Equation'Depends nt VariaNe: RESIDMethod: L&astSquaresDate: 11/C7/12 Time: 21:47Sample： 1973 2006Included observations:Presample missing jadum lagged res iduals set to zero.CoefficientStd Errort-S1atisticPrab-.C100.2419170.94

21、010.5864150.5629X-0.005102O.Oa&481-0.9307290.3009RESID(-1)1.4631020.1793258.15S 9260.0000RESIDES)0.6124S7&.524S4S-5 7257930.0116R-squaredi0 3157&4Mean depends nt var-169E-12Adjusted Ft-squarect0.793544S.D dependentvar1039 573S.E of regression472.2406Akaike inio criterion1620030Sum qiiard

22、 resid5575580.Schwarz criterion15.469S9Laglifeelihood-217.5643Hannan-Cuinn crrter.15.33936F-stati tic35,09501Durhin-Watsun statProb(F-staiistic)DOOOOOO從上面的輸出可知： LM=23.65686 , Prob.Chi-Square(2)=0.0000,小于=0.05，且輔助回 歸中RESID(-I)和RESID(-2)的系數(shù)均顯著不為 0 (對(duì)應(yīng)t統(tǒng)計(jì)量的P值均小于0.05),說明 模型具有2節(jié)序列相關(guān)。在 Equation 窗口，點(diǎn) View

23、Residual Tests Serial correlation LM Test ,在彈出的對(duì)話 框里將滯后階數(shù)改為3:點(diǎn)“OK”得到下面的輸出:E re u 5 chi -Go Sf re y 3 eri al Cgrr&latiQii LM T&stF-slatisticODsR-squared3803B6723.96054Prob- FC3.24)Prob Chi-Square(3)0.0000D.0000Test Equation:Dependent Variable RESIIDMethod: Least SquaresDate: 11/07/12 Time:21:

24、52Sample: 197S 2006Included obsenations: 29Pres ample missing value lagged rsiduals set to ero.CoefficientStd Errort-StatisticProbC29 00937179.48970.1616210.8730X-0.0023040.005S10-0.3A99030.7Q00R£SID-1)-1.3501960.2010186.7166020.0000RE8ID(-2)-0 2997S3034253C -0 8752030.3901RESIDE)”0 3063710.254

25、757-1.2025980.2409R-squaredD.S2&225LI esn depends nt var-1.B9E-12Adj ustod R-squared0.797253S.D dependentvar1039 573S.E. of regression468.0815Aka ike in1o criterion15.29075Sum squared resU525&斗。亂Schwarz criterion15.52649Leg livelihood-216.7158Hannan-Ouinn crii&r.15 36458F-slatistic28527&

26、amp;0Durbin-Watson stat1.B84232PiotHF-statistic)0.000000RESID(-2)2階序列相這時(shí)，LM=23.96054 , Prob.Chi-Square(2)=0.0000，小于 =0.05，但輔助回歸中 和RESID(-3)的系數(shù)不顯著(對(duì)應(yīng)t統(tǒng)計(jì)量的P值均大于0.05),說明模型僅存在 關(guān)，不具有3階的序列相關(guān)。3、序列相關(guān)的修正(1)廣義差分法已知模型具有2階序列相關(guān)，在命令行輸入命令:LS Y C X ARAR(2)回車得到下面的輸出：Dependant VariaWe： YMethod: L&a st SquaresDatK

27、l1rt)7/12 Time: 21:55Sample (adjusted): 1980 2006Included obsen/atians. 27 aftsr austmenisCan'/ergeftce achieved after 64 it&ratinsCoefficientStd £仃。t-StatisticProb,c13D348 826362230.049445D.9610X0.279594D064ES24.309250D.OOD3AR1.3902020.2130135.5263850.0000AR-0.3921790.233359-1.6805830.

28、1064R-squared0.998829Mean dependentvar15&56,37Adjusted R-squared0.99&676S.D dependentvar9324.072S.E of regression339.3329Akai ke info crite rion1462779Sum squared resid2648377.Schwarz criterion14.31977LoliKelitiood-193.4752卜knn an-Quin n crikr.倔&488F-statisticS536.974Dur bin-'. Vatson siat1.951415Pro b(P-statsticJ0.000000Inverted AR Roots1.00.39寫出修正后的模型：=130348.8+0.2796X+1.390