实验报告-序列相关性的分析与补救

实验报告---序列相关性分析名称：1960年至1992年居民的消费水平与可支配收入关系实验目的：掌握序列相关性的检验及处理方法实验内容：理论模型的设定：Y=β+βX+μ2.样本数据的收集：年份消费可支配收入年份消费可支配收入YXYX19601432.61569.219772829.83115.419611461.51619.419782951.6327619621533.81697.519793020.23365.519631596.61759.319803009.73385.719641692.31885.819813046.43464.919651799.12003.919823081.53495.6196619022110.619833240.63562.819671958.62202.319843407.63855.419682070.22302.119853566.5397219692147.52377.219863708.7410119702197.8246919873822.34168.219712279.52568.319883972.74332.119722415.92685.719894064.64416.819732532.62875.219904132.24498.219742514.72854.219914105.84500197525702903.619924219.84626.719762714.33017.6资料来源：《中国统计年鉴》1993，中国统计出版社3.模型参数的估计:通过OLS法建立消费与可支配收入之间的方程EViews软件估计结果如表1.2表1.2DependentVariable:YMethod:LeastSquaresDate:12/12/10Time:19:03Sample:19601992Includedobservations:33VariableCoefficientStd.Errort-StatisticProb.C-52.9184424.08305-2.1973320.0356X0.9179320.007526121.96320.0000R-squared0.997920Meandependentvar2757.545AdjustedR-squared0.997853S.D.dependentvar867.7769S.E.ofregression40.20706Akaikeinfocriterion10.28465Sumsquaredresid50114.84Schwarzcriterion10.37535Loglikelihood-167.6968F-statistic14875.01Durbin-Watsonstat0.788463Prob(F-statistic)0.000000Ŷ=-52.91844+0.917329X(-2.197)(121.963)R²=0.9979²=0.9978SE=40.2071D.W.=0.78854.模型的检验(即进行序列相关性检验)〔１〕做出残差项与时间的关系图如下：图1从残差项与时间t之间的关系图可以大致判断随机干扰项存在负序列相关性对其滞后一期的残差项做散点图，如下图2由残差项及滞后一期的残差项的关系图可以看出，随机干扰项存在正序列相关性。再由表1.2中的D.W.检验结果可知，在5%的显著性水平下，n=３３,k=2〔包括常数项〕，查表得＝１．３８，＝１．５１，由于Ｄ．Ｗ．＝０.７８８４６３＜，故随机干扰项存在正序列相关性。〔２〕，运用拉格朗日乘数检验，EViews软件估计２阶滞后残差项结果如表1.３表１．３Breusch-GodfreySerialCorrelationLMTest:F-statistic7.839487Probability0.001898Obs*R-squared11.58053Probability0.003057TestEquation:DependentVariable:RESIDMethod:LeastSquaresDate:12/12/10Time:19:39VariableCoefficientStd.Errort-StatisticProb.C-2.18412720.10792-0.1086200.9143X0.0009140.0062920.1451950.8856RESID(-1)0.5125060.1844142.7791050.0095RESID(-2)0.1309870.1865670.7020890.4882R-squared0.350925Meandependentvar-2.59E-13AdjustedR-squared0.283779S.D.dependentvar39.57384S.E.ofregression33.49127Akaikeinfocriterion9.973659Sumsquaredresid32528.29Schwarzcriterion10.15505Loglikelihood-160.5654F-statistic5.226324Durbin-Watsonstat1.931951Prob(F-statistic)0.005236由此表可知，含２阶滞后残差项的辅助回归为＝－２.１８４１２７＋０.０００９１４ｘ＋０．５１２５０６＋０．１３０９８７〔－０．１０９〕〔０．１４５〕〔２．７７９〕〔０．７０２〕R²＝０．３５０９２５于是，LM=31*0.350925=10.878675，该值大于显著水平为5%，自由度为2的分布的临界值〔2〕=5.991，由此判断原模型存在2阶序列相关性，但由于的参数t检验不通过，即参数不显著，说明不存在2阶序列相关性。5.运用广义差分法进行自相关的处理〔1〕采用科奥-迭代法估计ρ在EViews软件包下，1阶广义差分的估计结果如下表1.4表1.4DependentVariable:YMethod:LeastSquaresDate:12/12/10Time:19:50Sample(adjusted):19611992Includedobservations:32afteradjustingendpointsConvergenceachievedafter4iterationsVariableCoefficientStd.Errort-StatisticProb.C-72.6516151.16709-1.4198890.1663X0.9179320.01516360.892700.0000AR(1)0.5816830.1461903.9789650.0004R-squared0.998614Meandependentvar2798.950AdjustedR-squared0.998518S.D.dependentvar847.8975S.E.ofregression32.64164Akaikeinfocriterion9.898115Sumsquaredresid30898.82Schwarzcriterion10.03553Loglikelihood-155.3698F-statistic10444.12Durbin-Watsonstat2.179329Prob(F-statistic)0.000000InvertedARRoots.58与此估计结果可得：Ŷ=72.65161+0.917932*X+0.581683*AR〔1〕(-1.4199)(60.8627)(3.97897)=0.998614²=0.998518D.W.=2.179329其中，AR〔1〕前的参数值即为随机干扰项的1阶序列相关系数。在5%的显著性水平下，=1.5<D.W.=2.179329<4-=2.5,且各变量前的参数检验均通过，说明经广义差分后的模型已不存在序列相关性。与原模型相比，仅是截距项有差距，X前的参数没有差异。〔2〕采用杜宾两步法估计ρ第一步，估计模型=β+ρ+βX+βX+є在EViews软件包下，得出如下表1.4表1.4DependentVariable:YMethod:LeastSquaresDate:12/12/10Time:19:53Sample(adjusted):19611992Includedobservations:32afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.C-15.7571423.03522-0.6840450.4996Y(-1)0.6471530.1447174.4718450.0001X0.7380810.1007057.3291350.0000X(-1)-0.4097500.147759-2.7730910.0098R-squared0.998766Meandependentvar2798.950AdjustedR-squared0.998634S.D.dependentvar847.8975S.E.ofregression31.34150Akaikeinfocriterion9.844232Sumsquaredresid27504.11Schwarzcriterion10.02745Loglikelihood-153.5077F-statistic7553.554Durbin-Watsonstat1.894506Prob(F-statistic)0.000000由上表可得出：Ŷ=-15.75714+0.647153*+0.738081*X-0.409750*X〔-0.684〕(4.472)(7.329)(-2.773)=0.998766²=0.998634D.W.=1.894506第二步，作差分变换=+0.647153*X=X-0.409750*X那么，关于X的OLS估计结果如表1.5所示：表1.5DependentVariable:Y1Method:LeastSquaresDate:12/12/10Time:19:59Sample:19601992Includedobservations:33VariableCoefficientStd.Errort-StatisticProb.C-53.9417224.08600-2.2395470.0324X10.9179320.007526121.96320.0000R-squared0.997920Meandependentvar2756.898AdjustedR-squared0.997853S.D.dependentvar867.7769S.E.ofregression40.20706Akaikeinfocriterion10.28465Sumsquaredresid50114.84Schwarzcriterion10.37535Loglikelihood-167.6968F-statistic14875.01Durbin-Watsonstat1.788463