實驗報告-序列相關性的分析與補救

實驗報告---序列相關性分析名稱：1960年至1992年居民的消費水平與可支配收入關系實驗目的：掌握序列相關性的檢驗及處理方法實驗內容：理論模型的設定：Y=β+βX+μ2.樣本數據的收集：年份消費可支配收入年份消費可支配收入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資料來源：《中國統(tǒng)計年鑒》1993，中國統(tǒng)計出版社3.模型參數的估計:通過OLS法建立消費與可支配收入之間的方程EViews軟件估計結果如表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)0.000000?=-52.91844+0.917329X(-2.197)(121.963)R2=0.99792=0.9978SE=40.2071D.W.=0.78854.模型的檢驗(即進行序列相關性檢驗)〔１〕做出殘差項與時間的關系圖如下：圖1從殘差項與時間t之間的關系圖可以大致判斷隨機干擾項存在負序列相關性對其滯后一期的殘差項做散點圖，如下圖2由殘差項及滯后一期的殘差項的關系圖可以看出，隨機干擾項存在正序列相關性。再由表1.2中的D.W.檢驗結果可知，在5%的顯著性水平下，n=３３,k=2〔包括常數項〕，查表得＝１．３８，＝１．５１，由于Ｄ．Ｗ．＝０.７８８４６３＜，故隨機干擾項存在正序列相關性?！玻病?，運用拉格朗日乘數檢驗，EViews軟件估計２階滯后殘差項結果如表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階滯后殘差項的輔助回歸為＝－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，該值大于顯著水平為5%，自由度為2的分布的臨界值〔2〕=5.991，由此判斷原模型存在2階序列相關性，但由于的參數t檢驗不通過，即參數不顯著，說明不存在2階序列相關性。5.運用廣義差分法進行自相關的處理〔1〕采用科奧-迭代法估計ρ在EViews軟件包下，1階廣義差分的估計結果如下表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與此估計結果可得：?=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〕前的參數值即為隨機干擾項的1階序列相關系數。在5%的顯著性水平下，=1.5<D.W.=2.179329<4-=2.5,且各變量前的參數檢驗均通過，說明經廣義差分后的模型已不存在序列相關性。與原模型相比，僅是截距項有差距，X前的參數沒有差異?！?〕采用杜賓兩步法估計ρ第一步，估計模型=β+ρ+βX+βX+?在EViews軟件包下，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：?=-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，作差分變換=+0.647153*X=X-0.409750*X那么，關于X的OLS估計結果如表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