序列相关的检验和修正

序列相关的检验及修正例题：中国居民总量消费函数数据：年份GDPCONSCPITAXGDPCXY19783605.61759.146.21519.287802.66678.93806.819794092.62011.547.07537.828694.77552.14273.419804592.92331.250.62571.709073.37943.94605.319815008.82627.951.90629.899650.98437.25063.419825590.02902.952.95700.0210557.19235.15482.319836216.23231.154.00775.5911511.510075.25983.519847362.73742.055.47947.3513273.311565.46746.019859076.74687.460.652040.7914965.711600.87728.6198610508.55302.164.572090.3716274.613037.28211.4198712277.46126.169.302140.3617716.314627.88840.0198815388.67868.182.302390.4718698.215793.69560.3198917311.38812.697.002727.4017846.715034.99085.2199019347.89450.9100.002821.8619347.816525.99450.9199122577.410730.6103.422990.1721830.818939.510375.7199227565.213000.1110.033296.9125052.422056.111815.1199336938.116412.1126.204255.3029269.525897.613004.8199450217.421844.2156.655126.8832057.128784.213944.6199563216.928369.7183.416038.0434467.531175.415467.9199674163.633955.9198.666909.8237331.933853.717092.5199781658.536921.5204.218234.0439987.535955.418080.2199886531.639229.3202.599262.8042712.738140.519363.9199991125.041920.4199.7210682.5845626.440277.620989.6200098749.045854.6200.5512581.5149239.142965.622864.42001108972.449213.2201.9415301.3853962.846385.624370.22002120350.352571.3200.3217636.4560079.051274.926243.72003136398.856834.4202.7320017.3167281.057407.128034.52004160280.463833.5210.6324165.6876095.764622.730306.02005188692.171217.5214.4228778.5488001.274579.633214.02006221170.580120.5217.6534809.72101617.585624.136811.61、建立回归模型，模型的OLS估计Yt 0 1Xtt（1）录入数据打开EViews6，点“Fil”“New”“Workfil”

选择“Dated-regularfrequdbcy在Frequency后选择“Annual”，在Startda后输入1978,在Enddata后输入2006，点击“ok”在命令行输入：DATAXY，回车将数据复制粘贴到Group中的表格中:

Group:UKTITLEDTorkfile:KUL工EKLMTCGUAH::…口回区“小网.Pm匚,口用曰匚t.[PrinfNamsFfbbwe.Defaultv[5口HTrari印口5e[Edit+卜5mpl+/-6678.9obsXY19706678.9003306.00019797552.1004273.40019007943.9004605.30019010437.2005063.40019029235.1005482.300190310075.205983.500190411565.406746.000190511600.007720.600190613037.200211.400190714627.000040.000190015793.609560.300190915034.909085.200199016525.909450.900199110939.5010375.70199222056.1011815.10199325397.6013004.00199423784.2013944.601995^11754n154R7qn1996<|Hl>l(2)估计回归方程在命令行输入命令：LSYCX,回车或者在主菜单中点“Quick” “EstimateEquation在Specificati雨输入丫CX,“确定”。得到如下输出：Equation:UNTITLEDTorkfile:XULIEXIAHG...国回区UiswPm,口市以Prin；NmmsFrsBEs]DependentVariable:YMethod:LeastSquaresDate:06/03/12Time:18:13Sample:19782006Includedobservations:29CoefficientStd.Errort-StatisticProb.C2091.232334.9917 6.2427070.0000X0.4375270.009297 47.050370.0000R-squared0.987955Meandependentvar14855.72AdjustedR-squared0.987509S.D.dependentvar9472.093S.E.ofregression1053.650Akaikeinfocriterion16,83385Sumsquaredresid30259949Schwarzcriterion16,92014Loglikelihood-242.0900Hannan-Quinncriter.16,86330F-statistic2214.537Durbin-Watsonstat0.277132Prob(F-statistic)0.000000写出估计结果:Y2091.280.4375X(6.243) (47.059)R2=0.9880R20.9875 F=2214.537 D.W.=0.2772、序列相关的检验(1)图示检验法作残差序列的时序图：保存残差虚列：GENRE=RESID从图上可以看出，模型的最小二乘残差开始连续几期小于0，接着连续几期都大于0，这种模式的残差意味着模型可能存在正的序列相关性。做©和6的关系图：tt1SCATE(-1)E

2,400--1,600-4,0002,000-1,600-1,200-800-400-0--400--800--1,200-从上面的散点图可以看出,2,400--1,600-4,0002,000-1,600-1,200-800-400-0--400--800--1,200-从上面的散点图可以看出,et和21之间可以拟合一个线性模型:e=et11t表明模型存在正的序列相关性。且回归直线的斜率为正(>0)，表明模型存在正的序列相关性。34，(2)DW检验34，由OLS估计的结果可知:D.W.=0.277。查DW分布的临界值表，k=2,n=29时，dL=1.，=1.48,显然0<0.277<%,因此模型存在一阶正的自相关。(3)回归检验法拟合模型：e=e，并运用OLS估计模型：LSEE(-1)tt1t得到如下结果：OEquation:UNTITLEDWorkfile:XULIEX1ANGGUAN::U...且亘匿|始已神||P「0d|口bject|p「int||Name||F「Ee花|EstimateForecastStats||ResidsDependentVariable:EMethod:LeastSquares□ate:11/07/12Time:21:17Sample(adjusted):19792006Includedobservations:28afteradjustmentsCoefficientStd.Errort-StatisticProb.E(-1)0.94S9720.116460 8.1404910.0000R-squared0.710391Meandependentvar43,09574AdjustedR-squared0710391S.D.dependentvar1031.932S.E.ofregression555.3373Akaikeinfocriterion15,51209Sumsquaredresid8326787.Schwarzcriterion15,55967Loglikelihood-216.1693Hannan-Quinncriter.15,52663□urbin-Watsonstat0.576494写出回归结果：e0.949et t1(8.148)回归系数的t统计量为8.148伴随概率P=0.0000<=0.05,表明原模型存在一阶序列相关。拟合模型：e=ee ，并运用OLS估计模型：LSEE(-1)E(-2)t1t1 2t2t得到如下结果：DependentVariable:EMethod:LeastSquaresDate:11/07/12Time:21:24Sample(adjusted):19802006Includedobservations:27afteradjustmentsCoefficientStd.Errort-StatisticProb.1.6586910.152243 10.095000.0000-0.8643560.155255 -5.5673450.0000R-squared0864051Meandependentvar86,25222AdjustedR-squared0.858613S.D.dependentvar1025.517S.E.ofregression385.6093Akaikeinfocriterion1481372Sumsquaredresid3717374.SchwarzcriterionU.91470Loglikelihood-198.0527Hannan-Quinncriter.14,84726□urbin-Watsonstat2.317512写出回归结果：z 〜 〜e 1.659e 0.864et t1 t2(10.895)(-5.567)回归系数:1和：2的t统计量分别为10.895,-5.567相应的伴随概率P=0.0000<=0.05,

表明原模型存在二阶序列相关。，并运用OLS估计模型:LSEE(-1)E(-2)t，并运用OLS估计模型:LSEE(-1)E(-2)t£(-3)回车，得到如下结果:DependentVariable:EMethod:LeastSquares□ate:11/07/12Time:2136Sample[adjusted):19812006Includedobservations:26afteradjustmentsCoefficientStd.Errort-StatisticProb.E(-1)14953670.205421 7.2795340.0000E(-2)-0.4-741000.371327 -1.2767720.2144E『3)-0.2060350.241900 -1.1824510.2491R-squared0.867062Meande口endentva「126.5562AdjustedR-squared0.855502S.D.dependentvar1023.787S.E.ofregression3S9.1710Akaikeinfocriterion1437408Sumsquared「esid3433444.Schwarzcriterion15,01925Loglikelihood-1903631Hannan-Quinncriter.14,91583Durbin-Watsonstat2.170417写出回归结果:1.49510.474(7.280)(-1.277) (-1.18)回归系数:1的t统计量为7.280相应的伴随概率P1=0.0000<=0.05表明:1显著不为零，但P2和0的t统计量分别为-1.277-1.182相应的伴随概率P2=0.2144,P3=0.2491，均大于=0.05表明原模型不存在三阶序列相关。综上，原模型有二阶序列相关。(4)LM检验首先采用OLS估计模型，在弹出的Equation窗口，点ViewResidualTestsSerialcorrelationLMTest♦弹出下面的对话框：点“OK”得到下面的输出：Breusch-GodfreySerialCorrelationLMTestF-statistic55,34401Prob.F(2,25)0.0000Obs*R-squared2365636Prob.Chi-Square{2}0.0000TestEquation:□ependentVariable:RESIDMethod:LeastSquaresDate:11/07/12Time:21:47Sample:19732006Includedobservations:29Presamplemissingvaluelaggedresidualssettozero.CoefficientStd.Errort-StatisticProbc100.2419170.94-010.5864150.5629X-0.0051020.005481-0.93072903609RESIDf-1)14531020.1793258.1589260.0000RESID(-2)-0.6124870.224948-2.7227930.0116R-squared0815754Meandependentvar-1.69E-12AdjustedR-squared0.7936US.D.dependentvar1039.573S.E.ofregression472.2406Akaikeinfocriterion15,23030Sumsquaredresid5575230.Schwarzcriterion15-46889Loglikelihood-217.5643Hannan-Quinncriter.15.33936F-statistic36,39601Durbin-Watsonstat1.946335ProbfF-statistic}0.000000从上面的输出可知：LM=23.65686,Prob.Chi-Square(2)=0.0Q0小于=0.05,且辅助回归中RESID(-1)和RESID(-2)的系数均显著不为0(对应t统计量的P值均小于0.05)，说明模型具有2节序列相关。在Equatior窗口，点ViewResidualTestSSerialcolationLMTest，••在弹出的对话框里将滞后阶数改为3：点“OK”得到下面的输出:

Breusch-GodfreySerialCorrelationLMTest:F-statistic33,03667Prob.F(3,24)0.0000Obs^R-squared23,96054Prob.Chi-Square(3)0.0000TestEquation:DependentVariable:RESIDMethod:LeastSquares□ate:11/07/12Time:21:52Sample:19782006Includedobservations:29Presamplemissingvaluelaggedresidualssettozero.CoefficientStd.Errort-StatisticProb.C29,00937179.4397 0.1616210.3730X-0.0023040.005910 -0.3399030.7000RESID(-1)1.3901960.201013 6.7168020.0000RESID(-2)-0.2997830.342530 -0.37520S0.3901RESID(-3}-0.3063710.254757 -1.2025980.2409R-squared0.326225Meandependentvar-1.69E-12AdjustedR-squared0.79726SS.D.dependentvar1039.573S.E.ofregression468.0815Akaikeinfocriterion15,29075Sumsquaredresid5253408.Schwarzcriterion15,52649Loglikelihood-216.7158Hannan-Quinncriter.1536458F-statistic23,52750Durbin-Watsonstat1.864232Prob(F-statistic}0.000000这时,LM=23.96054,Prob.Chi-Square(2)=0.0Q小于=0.05,但辅助回归中RESID(-2)和RESID(-3)的系数不显著(对应t统计量的P值均大于0.05)，说明模型仅存在2阶序列相关，不具有3阶的序列相关。3、序列相关的修正(1)广义差分法已知模型具有2阶序列相关，在命令行输入命令：LSYCXAR(1)AR⑵回车得到下面的输出：DependentVariable:YMethod:LeastSquaresDate:11/07/12Time:21:56Sample(adjusted):19802006Includedobservations:27afteradjustmentsConvergenceachievedafter64iterationsCoefficientStd.Errort-StatisticProb.C13034S.32636223. 0.0494450.9610X0.2795940.064382 4.3092590.0003AR[1)1.3902020.213013 6.5263850.0000AR[2)-0.392179口.233359 -1.6305830.1064R-squared0.990829Meandependentvar15656.87AdjustedR-squared0.993676S.D.dependentvar9324.872S.E.ofregression3393329Akaikeinfocriterion14,62779Sumsquaredresid2648377.Schwarzcriterion14,31977Loglikelihood-193.4752Hannan-Quinncriter.14,63488F-statistic6536974□urbin-Watsonstat1.951415Prob(F-statistic)0.000000InvertedARRoots1.0039写出修正后的