實(shí)驗(yàn)報(bào)告-序列相關(guān)性的分析與補(bǔ)救

實(shí)驗(yàn)報(bào)告---序列相關(guān)性分析名稱：1960年至1992年居民的消費(fèi)水平與可支配收入關(guān)系實(shí)驗(yàn)?zāi)康模赫莆招蛄邢嚓P(guān)性的檢驗(yàn)及處理方法實(shí)驗(yàn)內(nèi)容：理論模型的設(shè)定：Y=β+βX+μ2.樣本數(shù)據(jù)的收集：年份消費(fèi)可支配收入年份消費(fèi)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(lái)源：《中國(guó)統(tǒng)計(jì)年鑒》1993，中國(guó)統(tǒng)計(jì)出版社3.模型參數(shù)的估計(jì):通過(guò)OLS法建立消費(fèi)與可支配收入之間的方程EViews軟件估計(jì)結(jié)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(yàn)(即進(jìn)行序列相關(guān)性檢驗(yàn))〔１〕做出殘差項(xiàng)與時(shí)間的關(guān)系圖如下：圖1從殘差項(xiàng)與時(shí)間t之間的關(guān)系圖可以大致判斷隨機(jī)干擾項(xiàng)存在負(fù)序列相關(guān)性對(duì)其滯后一期的殘差項(xiàng)做散點(diǎn)圖，如下圖2由殘差項(xiàng)及滯后一期的殘差項(xiàng)的關(guān)系圖可以看出，隨機(jī)干擾項(xiàng)存在正序列相關(guān)性。再由表1.2中的D.W.檢驗(yàn)結(jié)果可知，在5%的顯著性水平下，n=３３,k=2〔包括常數(shù)項(xiàng)〕，查表得＝１．３８，＝１．５１，由于Ｄ．Ｗ．＝０.７８８４６３＜，故隨機(jī)干擾項(xiàng)存在正序列相關(guān)性?！玻病?，運(yùn)用拉格朗日乘數(shù)檢驗(yàn)，EViews軟件估計(jì)２階滯后殘差項(xiàng)結(jié)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(xiàng)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(guān)性，但由于的參數(shù)t檢驗(yàn)不通過(guò)，即參數(shù)不顯著，說(shuō)明不存在2階序列相關(guān)性。5.運(yùn)用廣義差分法進(jìn)行自相關(guān)的處理〔1〕采用科奧-迭代法估計(jì)ρ在EViews軟件包下，1階廣義差分的估計(jì)結(jié)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(jì)結(jié)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(shù)值即為隨機(jī)干擾項(xiàng)的1階序列相關(guān)系數(shù)。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(shù)檢驗(yàn)均通過(guò)，說(shuō)明經(jīng)廣義差分后的模型已不存在序列相關(guān)性。與原模型相比，僅是截距項(xiàng)有差距，X前的參數(shù)沒(méi)有差異?！?〕采用杜賓兩步法估計(jì)ρ第一步，估計(jì)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(guān)于X的OLS估計(jì)結(jié)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