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1、关键词：食品价格指数多因素分析预测模型模型检测与修正二、模型设定在本文中，我们选取粮食价格指数、肉禽及制品价格指数、水产品价格指数、蔬菜价格指数作为解释变量，选取食品价格指数作为被解释变量，构建多元线性回归模型:Y二BOB1X1+B2X2+B3X3+B4X4+ui其中：Y食品价格指数Xl粮食价格指数X2肉禽价格指数X3水产品价格指数X4蔬菜价格指数三、模型的估计与调整通过使用Eviews计量经济学分析软件，得到了一下回归分析结果DependentVariableiYMethodzLeastSquaresDate:05/03/14Time:19:50Sample:2014:012014:04In
2、cludedobservations:27VariableCoefficientStd.Errort-StatisticProb.C7.2991204.8192871.5145640.1441Xl0.4531110.0604837.4915(X)().()(MX)X20.2255630.02100210.740120.0000X30.1764920.()642352.7475760.0118X40.0593710.0123924.7909120.0001R-squared0.990031Meandependentvar108.2515AdjustedR-squared0.988219S.D.d
3、ependentvar4.152074S.E.ofregression0.450673Akaikeinfbcriterion1.409427Sumsquaredresid4.468336Schwarzcriterion1.649396Loglikelihood-14.02726F-546.2222Durbin-Watsonstat0.901780Prob(F-Statistic)0.0000001.多重共线性检验。CorreIationMatrixYXlX2X3X4Y1.0000000804G1209393210963383-0S3928GX10.8046121.0000000.6162700
4、.79G154-0.6G6700X20.9-39-32106162701.0000000S32967-0.742045X30.363-3830.7961540.S829G71.000000-0.590632X4-0.63928B-0666700-074204-6-06908321.000000(1)直观的来看，xl、X3的相关系数达到了0.80,x2、x3的相关系数达到了0.88o所以可以认为存在较严重的多重共线性。(2)修正多重共线性现剔除x3进行回归，结果如下：DependentVariableiYMethodiLeastSquaresDate:05/03/14Time:21:40Samp
5、le:2014:012014:04InCIUdedobSerValionS:27VariableCoefficientStd.Error1-StatisticProb.C5.2102285.3941020.9659120.3441Xl0.5787620.04486712.899600.0000X20.2749320.01232422.308120.0000X40.0758200.0122986.165094().(XX)()R-squared0.986610Meandependentvar108.251AdjustedR-squared0.984864S.D.dependentvar4.152
6、07S.E.ofregression0.510823Akaikeinfocriterion1.63036Sumsquaredresid6.001621Schwarzcrilerion1.82234Loglikelihood-18.00994F-statistic564.920Durbin-Watsonstat0.921999Prob(F-Statistic)().(X)(MX)由上图可看出，剔除x3后,拟合优度非常好，且显著性明显。再剔除l进行回归，结果入下:DependentVariable:YMethodiLeastSquaresDate:05/03/14Time:21:43Sample:
7、2014:012014:04lncludedobservations:27VariableCoefficientSld.Error1-StatisticProb.C32394936.3853025.073358().(MX)()X20.1426790.0329004.3367320.0002X30.54()3430.0774786.974153().(XX)0X40.0144350.0199850.7222650.4774R-squaredAdj us ted R- sq uared0.9646010.959983Meandependentvar108.2515S.D.dependentvar
8、4.152074S.E.ofregression0.830589Akaikeinfbcriterion2.602589Sumsquaredresicl15.86718Schwarzcriterion2.794565Loglikelihood-31.13496F-statistic208.9094Durbin-Watsonstat1.044482Prob(F-Statistic)0.000000由上图可以看剔除Xl导致x4通不过t检验。剔除x2进行回归，结果如下：DependentVariabIerYMethodzLeastSquaresDate:05/03/14Time:21:41Sample
9、:2014:012014:04Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.C16.3409511.595881.4092020.1722Xl().11()9050.1256320.8827720.3865X30.7667330.0812689.4346090.0000X4-0.0321650.021984-1.4630590.1570R-squared0.937763varMeandependent108.2515AdjustedR-Squared0.929645S.D.dependentvar4.152
10、074S.E.ofregressionI.101317Akaikeinfo3.166844criterionSumsquaredresid27.89668Schwarzcriterion3.358820Loglikelihood-38.75239F-statistic115.5183Durbin-Watsonstat1.495176Prob(F-Statislic)0.000000由上图可知，剔除x2后，导致xl,x4都通不过t检验，且可决系数大幅降低。剔除x4进行回归，结果入下：DependentVariablerYMethodzLeastSquaresDate:05/03/14Time:2
11、1:44Sample:2014:012014:04Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.C21.060075.4100843.8927440.0007Xl0.3128540.0739924.2282150.0003X20.1563630.0213157.3358800.0000R-squared0.979631Meandependentvar108.2515AdjustedR-Squared0.976974S.D.dependentvar4.152074S.E.ofregression0.63005
12、2Akaikeinfocriterion2.049924Sumsquaredresid9.130200Schwarzcriterion2.241900Loglikelihood-23.67397F-statistic368.7162Durbin-Watsonstat2.010366Prob(F-Statistic)0.000000X303251700.0786274.1355880.00()4由上图可看出，x4的存在不影响本文的分析结果,没必要剔除。所以综上所述，剔除x3,得到一下回归分析结果:DependentVariable:YMethodrLeastSquaresDate:05/31/1
13、2Time:21:40Sample:2014:012014:04Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.C5.2102285.3941020.9659120.3441Xl0.5787620.04486712.899600.0000X20.2749320.01232422.308120.0000X40.0758200.0122986.1650940.0000R-squared0.986610Meandependentvar108.2515AdjusiedR-Squared0.984864S.D.depe
14、ndentvar4.152074S.E.ofregression0.510823Akaikeinfocriterion1.630366Sumsquaredresid6.001621Schwarzcriterion1.822342Loglikelihood-18.00994F-564.9205Durbin-Watsonstat0.921999Prob(F-Statistic)0.000000得到的回归方程为y=5.210228+0.578762X1+0.274932X2+0.07582X4(0.965912)(12.8996)(22.3081)(6.165094)R2=0.9866Adjuste
15、dR-squared=0.9849F=564.9205从回归的结果可以得到R2=0.9866,修正的可决系数为0.9849,这说明模型对样本的拟合度非常好。2 .相关性检验从估计的结果可以看出，模型拟合较好，可决系数R2R.9866,修正的可决系数为0.9849,表明模型在整体上拟合比较好。1*120 nsResidualActualFitted3 .显著性检验(1)对于BLt统计量为12.8996。给定a=0.05,查t分布表，在自由度为n-4=23下，得临界值10.025(23)=2.069,因为tt.025(23),所以拒绝原假设HO:Bl=0,表明粮食价格指数对食品价格指数有显著性影响
16、；(2)对于B2,t统计量为22.3081。给定0.05,查t分布表，在自由度为。-4二23下，得临界值10.025(23)=2.069,因为tt.025(23),所以拒绝原假设H0:B2=0,表明肉禽价格指数对食品价格指数有显著性影响。(3)对于B4,t统计量为6.165094。给定0.05,查t分布表，在自由度为限4二23下,得临界值t.025(23)=2.069,因为tt.025(23),所以拒绝原假设H0:B4=0,表明蔬菜价格指数对食品价格指数有显著性影响。(4)对于F=564.9205F23)=3.03(显著性水平为0.05),表明模型从整体上看食品价格指数与各解释变量之间线性关系
17、显著。4序列相关检验ACPACQ-StatProbAutocorrelationPartiaICorreIation10.6190.6198.10670.0042-0037-0.4198.14S80.0173-0.428-0.30514.1200.0034-CRaa-CoaooRn06-0.444-0.225320220.0006-00-590.03532.1520.000/0.197-0.196336570.00080.234-021835.9220.00090.127-0.21636.6220.000100061-0.0373G.7920.000110.1430.27237.7890.00
18、0120019-0.29137.8090.000(1)由图可知，存在一阶自相关。(2)修正:用科克伦-奥克特迭代方程法对模型进行修正，得到如下结果:DependentVariableiYMethodZLeastSquaresDate:05/03/14Time:13:10Sample(adjusted):2014:012014:04Includedobservations:26afteradjustingendpointsCOnVergenCeaChieVedafIerlOiterationSVariableCoefficientStd.Errort-StatisticProb.C5.16918
19、79.8464600.5249790.6051Xl0.5631620.0877866.415188().()(XX)X20.2821290.01771215.928550.0000X40.0845860.01033()8.188270().()(XX)AR(I)0.5840820.1869773.1238250.0051R-squared0.989380Meandependentvar108.5496AdjustedR-Squared0.987357S.D.dependentvar3.928543S.E.ofregression0.441736Akaikeinfocriterion1.3748
20、31Sumsquaredresid4.097737Schwarzcriterion1.616772Loglikelihood-12.87280F-489.0816Durbin-Watsonstat1.380596Prob(F-Statistic)0.000000InvertedARRoots.58得到一阶自相关系数估计为0.584082再次检验是否存在自相关：AutocorrelationPartiaICorreIationACPACQ-StatProb1j1110.2980.2982.57971I1i12-0.120-0.229301970.032IL1i13-0.309-0.228S.04
21、930.049I:1i14-0.358-0.25810.2970.01EiL1匚1E-0.335-0.315141770.00711116-0.014-0.043141B40.01411110.W2-0.1081S.1920.01911I1S0165-0.1351&.2990.02311I19O.OS1-0.1531&.5810.035111100.001-0.1521&.5810.056111二11101950.2S718.4200.040111/2-0.002-0.12218.4200.072L由上图可知，修正后不再存在自相关。综上，本研究模型估计的最终结果为得到的回归方程为丫=5/691
22、+0.5631X1+0.2821X2+0.0846X4(0.5250)(6.4152)(15.9286)(8.1883)R2=0.9894AdjustedR-squared=0.9874F=489.0816经济意义检验：从经济意义上来看,该模型说明了在假定其他变量不变的情况下，粮食价格指数每上升1乐食品价格指数上涨0.5631%；肉禽及制品价格指数每上升1%,食品价格指数上涨0.2821%；蔬菜价格指数每上升1%,食品价格指数上涨0.0846%。由于各变量都通过了检验，所以说明各变量对被解释变量都起到了很好的作用。5因果关系检验对xl，y进行因果关系检验，结果如下：PairwiseGrange
23、rCausalityTestsDale:05/03/14Time:21:54Sample:2014:012014:()4JUNullHypolhesis:ObsF-StatisticProbabilityY(IoesnotGrangerCauseX1X1doesnotGrangerCauseY251.094032.866370.354090.08043由上图可知，选定显著性水平(如10%),0.350.1,则在该显著性水平下，接受原假设，表示食品价格指数对粮食价格指数没有影响；0.080.1理在该显著性水平下，接受假设，表示食品价格指数对肉禽价格指数没有影响；0.30.1,接受原假设，表示粮食
24、价格指数对食品价格指数没有显著性的影响。对x4,y进行因果关系检验，结果如下:PairuqseGrangerCausalityTestsDate:05/03/14Time:20:36Sample:2014:012014:041.agS:4NuIlHypothesis:ObsF-StatisticProbabilityYdoesnotGrangerCauseX4235.128760.00932XddoesnotGrangerCauseYL403010.28366由上图可知，选定显著性水平10%)0.0090.1,接受原假设，表示蔬菜价格指数对食品价格指数没有影响。四、结论及政策建议本研究的结果表明，食品价格指数确实受到粮食价格指数、肉禽及其制品价格指数、蔬菜价格指数四个因素的影响，从经济意义上来看,该模型说明了在假定其他变量不变的情况下，粮食价格指数每上升1%,食品价格指数上涨0.5631%；肉禽及制品价格指数每上升设，食品价格指数上涨0.2821乐蔬菜价格指数每上升1幅食品价格指数上涨0.0846%o由于各变量都通过了检验，所以说明各变量对被解释变量都起到了很好的解释作用。
