序列相關的檢驗和修正

1、序列相關的檢驗及修正例題：中國居民總量消費函數纏：年份GDPCONSCPITAXGDPCXY19783605.61759.146.21519.287802.66678.93806.819794092.62011.547.07537.828694.77552.14273.419804592.92331.250.62571.709073.37943.94605.319815008.82627.951.90629.899650.98437.25063.419825590.02902.952.95700.0210557.19235.15482.319836216.23231.154.00775.591

2、1511.510075.25983.519847362.73742.055.47947.3513273.311565.46746.019859076.74687.460.652040.7914965.711600.87728.6198610508.55302.164.572090.3716274.613037.28211.4198712277.46126.169.3021403617716.314627.88840.0198815388.67868.182.302390.4718698.215793.69560.3198917311.38812.697.002727.4017846.71503

3、4.99085.2199019347.89450.9100.002821.8619347.816525.99450.9199122577.410730.6103.422990.1721830.818939.510375.7199227565.213000.1110.033296.9125052.422056.111815.1199336938.116412.1.204255.3029269.525897.613004.8199450217.421844.2156.655126.8832057.128784.213944.6199563216.928369.7183.416038.0434467

4、.531175.415467.9199674163.633955.9.666909.8237331.933853.717092.5199781658.536921.5204.218234.0439987.535955.418080.2199886531.639229.3202.599262.8042712.738140.519363.9199991125.041920.4.7210682.5845626.440277.620989.6200098749.045854.6200.5512581.5149239.142965.622864.42001108972.449213.2201.94153

5、01.3853962.846385.624370.22002120350.352571.3200.3217636.4560079.051274.926243.72003136398.856834.4202.7320017.3167281.057407.128034.52004160280.463833.5210.6324165.6876095.764622.730306.02005188692.171217.5214.4228778.5488001.274579.633214.02006221170.580120.5217.6534809.72101617.585624.136811.61、建

6、立回歸模型，模型的OLS估計X = 0o +0】X+“錄入打開 EViews6 ,點 Tile New Workfile選擇 nDated-regular frequency1 # 在 Frequency 后選擇Annual，在 Start data 后輸入1978 ,在End data后輸入2006 點擊在命令行輸入：DATA X Y,回車 將數據復制粘貼到Group中的表格中: Group; UMTITLED Torkfile; XTJLIEXIA1TGGWR ;口回岡苗&忡 | Proc object Print Name： Freeze Default v | Sort) Transp

7、ose! Edit+/-|5rnpl-t-/-|p8678.9obsXY19786678.9003806.800a19797552.1004273.40019807943.9004605.300|尋19818437.2005063.40019829235.1005482.300198310075.205983.500198411565.406746.000198511600.807728.600198613037.208211.400198714627.808840.000198815793.609560.300198915034.909085.200199016525.909450.9001

8、99118939.5010375.70199222056.1011815.10199325897.601 3004.80199428784.201 3944.601995anflfl71996 .：(2)估計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QuickEstimate Equation11，在 Specification 中輸入 Y C X ,點確走。得到如下輸出: Equation: UHTITLED Torkfile: XULIEKIA1I&. 口問岡伽訓Proc|0bjMtJ PrintE$timateeest匡at$R藥ids Dependent Vari

9、able: YMethod: Least SquaresDate:06X08J12 Time: 18:13Sample: 1 978 2006In eluded observati ons: 29CoefficientStd. Errort-StatisticProb.C2091.282334.99176.2427870.0000X0.4375270.00929747.058870.0000R-squared0.987955Mean dependent 妙1 4855.72Adjusted R-squared0.9875093.D. dependent var9472.098S.E. ofre

10、gression1058.650Akaike info criterion1 6.83385Sum squared resid30259949Schwarz criterion1 6.92814Log likelihood-242.0908Hannan-Quin n criter.1 6.86338F-statistic2214.537Durbin-Watson stat0.277132Prob(F-statisiic)0.000000寫出估計結果:y = 2091 28 + 0.4375 X(6.243 )(47.)F=2214.537D.W=0.277Q =0.9880 R1 =0.987

11、52、序列相關的檢驗(1)圖示檢驗法作殘差序列的時序圖：保存殘差虛歹IJ : GENR E=RESID作圖：PLOT E3.000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 ,接看連續(xù)幾期都大于0 , 這種模式的殘差意味著模型可能存在正的序列相關性。做和百“的關系圖：SCAT E(-l) E2,400-1,6002,000 -1,600-1,200-800-400-0-400-800-1,200-2,0002,000 4?0004,000E從上面的散點圖可以看出，E和之間可以擬合一個線性模型:且回歸直線的斜率為正(0 ),表明模型存在正的序列相關性。(2) DW檢驗由OLS估計的結果

12、可知：D.W-0.277。查DW分布的臨界值表，k=2 , n=29時,e/L=1.34 , =1.48 ,顯然0v0277v心，因此模型存在一階正的自相關。(3)回歸檢驗法擬合模型： = pet_ + 6 ,并運用OLS估計模型:LS E E(-l)得到如下結果： Equation: UNTITLED Workfile! XUUEXIANGGUAN：!U.| = | 回|viewproc|object |Print|(Name(FreezeForecast Stats,Resids|Dependent Variable: EMethod: Least SquaresDate: 11/07/1

13、2 Time: 21:17Sample (adjusted): 1979 2006Included observations: 28 after adjustmentsCoefficient Std. Error t-StatisticProb.E(-1)0.9489720.1164608.1484910.0000R-squared0.710391Mean dependentvar43.09574Adjusted R-squared0.710391S.D. dependentvar1031.932S E. of regression555.3373Aka ike info criterion1

14、5.51209Sum squared resid8326787.Schwarz criterion15.55967Log likelihood-216.1693Hannan-Quinn criter.15.52663Durbin-Watson stat0.576494寫出回歸結果：e, =0.949玄_(8.148 )回歸系數的t統計量為8.148 #伴隨概率P=0.0000 =0.05，表明原模型存在一階序 列相關。擬合模型：=戸電|+心-2+，并運用OLS估計模型：LS E E(-l) E(-2)得到如下結果：DependentVaiiable: EMethod: Least Square

15、sDate: 11/07/12 Time: 21:24Sample (adjusted): 1980 2006Included observations: 27 after adjustmentsCoefficientStd. Errort-StatisticProb.E(-1)1.6586910.15224310.895000.0000E(-2)-0.8643560.155255-5.5673450.0000R-squared0.864051Mean dependentvar86.25222Adjusted R-squared0.858613S.D. dependent var1025.51

16、7S.E. of regression385.6098Akaike info criterio n14.81872Sum squared resid3717374.Schwarz criterion14.91470Log likelihood-198.0527Han nan-Q uinn criter.14.84726Durbin-Waison stat2.317512寫出回歸結果：=1.659-0.864?(10.895 ) (-5.567)回歸系數和的t統計星分別為10.895、-5.567，相應的伴隨概率P=0.0000羽里盤來。MH-洞竊雌皿口孚羽里盤來。(4 ) LM 1OLSm斗肅

17、睦 IKS Equation 岡口=DIView Residua 一 Tesis Seria一 corre-ation LM Tesr、s圧F 回SX4-Breusch-Godfrey Serial Correlation LM Test:statistic55.34401Prob. F(2,25)0.0000Ot)s*R-squared23.65686Prob. Chi-Square(2)0.0000Test Equation:Dependent Variable: RESIDMethod: LeasiSquaresDate: 11/07/12 Time: 21:4-7Sample: 197

18、8 2006In eluded observati ons: 29Presample missing value lagged residuals set to zero.CoefficientStd. Errort-StatisticProb.c100.2419170.94010.5864150.5629X-0.0051020.005481-0.9307290.3609RESID (-1)1.4631020.1793258.1589260.0000RESID (-2)-0.6124&70.224-948-2.7227930.0116R-squared0.815754Mean dependen

19、tvar-1.69E-12Adjusted R-squared0.79364-4S.D. dependent燉1039.573S.E. of regression472.2406Akaike info criterion15.28030Sum squared resid5575280.Schwarz criterion15.46889Log likelihood-217.5643HannarvQuinn enter.15.33936F-statistic36.89601Dur&in-Watson stat1.946385Prob(F-staiistic)0.000000從上面的輸出可知：LM=

20、23.65686 , Prob.Chi-Square(2)=0.0000 r 小于 =0.05 f且輔助回歸中RESID(-l)和RESID(-2)的系數均顯著不為0 (對應t統計呈的P值均小于 0.05 ) r說明模型具有2節(jié)序列相關。在 Equation 窗口，點 View Residual Tests Serial correlation LM Test.,在彈 出的對話框里將滯后階數改為3 :點OK。彳導到下面的輸出：Breusch-Gocifrey Serial Correlation LM Test;F-statistic38.03667Prot. F(3,24)0.0000Obs

21、*R-squared23.96054Prob. Chi-Square(a)0.0000Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 11/07/12 Time: 21:52Sample: 1978 2006Included observations: 29Presample missing value lagged residuals set to zero.CoefficientStd. Errort-StatisticProt.C29.00937179.48970.1616210.8730X-0.0023

22、040.005910-0.3899030.7000RESID(-1)1.3501960.2010186.7168020.0000RESID (-2)-0.2997830.342530-0.8752030.3901RESID (-3)-0.3063710.254757-1.2025980.2409R-squared0.826225Mean dependentvar-1.69E-12Adjusted R-squared0.797263S.D. depende1039.573S.E. of regress ion468.0815AKaiKe info criter ion15.29075Sum sq

23、uared resid5258408.Schwarz criterion15.52649Log likelihood-216.7158Hannan-Quinn criter.15.36458F-statistic28.52750Durbin-Watson stat1.864232Prob(F-statistic)0.000000這時 r LM=23.96054 f Prob.Chi-Square(2)=0.0000 ,小于 =0.05，但輔助回歸 中RESID(-2)和RESID(3)的系數不顯著(對應t統計呈的P值均大于0.05 ),說明模型僅 存在2階序列相關,不具有3階的序列相關。3、序

24、列相關的修正(1)廣義差分法已知模型具有2階序列相關，在命令行輸入命令:LS Y C X AR(1) AR(2)回車 得到下面的輸出：Dependent Variable: YMethod: Least SquaresDate: 11/07/12 Time: 21:56Sample (adjusted); 1980 2006Included observations: 27 after adjustmentsCon vergence achieved after 6 4- iterationsCoefficientStd. Errort-StatisticProb.c130348.826362

25、23.0.0494450.9610X0.2795940.0648824.3092590.0003AR(1)1.3902020.2130136.5263850.0000AR(2)-0.3921790.233359-1.6805830.1064R-squared0.998829【viean dependent var15656.87Adjusted R-squared0.998676S.D. dependentv蔭9324.872S.E. of regression339.3329AKaike info criterion14.62779Sum squared resid2648377.Schwarz, criterion14.81977Log likelihood-193.4752Hann an-Quinn criter.14.68488F-statistic6536.974Durbin-Watson stat1.951415Prob(F-staiistic)0.000000Inverted AR Roots1.00.39寫出修正后的模型：=130348.8+0.2796X+1.3902AR(l)-0.3922AR(2)(0.049)(4.309)(6.52