计量经济学自相关性检验实验报告

1、计量经济学自相关性检验实验报告实验内容：自相关性检验工业增加值主要由全社会固定资产投资决定。为了考察全社会固定资产投资对工业增加值的影响，可使用如下模型：Yi= 0 iXi；下表列出了Y的统计数其中，X表示全社会固定资产投资，Y表示工业增加值。中国1998-2000的全社会固定资产投资 X与工业增加值据。年份固定资产投资X工业增加值丫年份固定资产投资X工业增加值丫1980910.91996.519915594.58087.119819612048.419928080.110284.519821230.42162.3199313072.314143.819831430.12375.6199417

2、042.119359.619841832.92789199520019.324718.319852543.23448.7199622913.529082.619863120.63967199724941.132412.119873791.74585.8199828406.233387.919884753.85777.2199929854.735087.219894410.46484200032917.739570.3199045176858单位:亿元、估计回归方程Dependent Variable: VMethod: Least SquaresDale： 12/22/09 Time: 05.

3、53Sample: 1980 2000Included obseivaiions: 21VariableCoeffi 匚 lentStd. Error t*StatisticProb.CBBS.0114298 16732240392 .372X1,1018610.019344 G 1.09630OJDQO口-squared0.59493GMean dep endent vrar13744.09Adjusted R-squared0,994669S”D” dependen! var13029.80S.E. of regression951.3338Akaike info criterion1S.

4、G4401Sum squared resid17195BB4Schwarz criterion16.7349Log likelihood-172 7G21F-stall Stic3732.753Durbin-Walson stat1.282353ProbF-stalistic)D.DOODDOOLS法的估计结果如下:Y=668.0114+1.181861X(2.24039) (61.0963)R2 =0.994936, R 2 =0.994669, SE=951.3388, D.W.=1.282353。二、进行序列相关性检验(1) 图示检验法3000 r 2000 1OOO -j *-1000

5、 - -2000 -10OO 20003000-3000,-3000 -2000 -QOO O通过残差与残差滞后一期的散点图可以判断， 随机干扰项存在正序列相关性。(2) 回归检验法一阶回归检验Dependent Variable: EMethod: Least SquaresDate;Time; 09:413arTiple(adjusted): 19B1 2000Included observations: 20 after adjusting endpointsVariableCoefficientStd Errort-5tatisticProbEC-1.3569760.213046693

6、200.1114R-squaredAdjustecJ 只-3qua red 3. E. of regression Sum squared resid Leg liikelihood127744127744386.776114941067 -1G3.G177Mean eJep巳rident var 3.D. dependent v刁r Akaika info 匚iterionSchwarz criterion Durbir-Walson st日t-12.59656949.493516.4617716,511661 5827EGet=0.356978et-1 + t二阶回归检验Depienden

7、t Variable: EMethod: Least SquaresDate 12/22/09 Time: 09:41Sainplefadjusted): 1902 2000Included observations: 19 after adjusting end pointsVariableCoefficisritStd. Errort-StatisticProb.E(-1)0.5724330.W55872.9267460.00943-0.6078310J99S16-3 0450030 QD73R-squared0.434191Mear dep endent vsr-26.13432Adju

8、sted 口-squared0.400908S,D dependent var9735267S.E. of regression753.5196Akaike info criterion旧EB日Sum stiuared resid9552459.Sohvvarz criterionie.23G10Log likelihood-151.7735Duirbin-Watsan start2 530753et =0.572433巳一1 0.607831_2 + t可见：该模型存在二阶序列相关。(3) 杜宾-瓦森(D.W)检验法由OLS法的估计结果知：D.W.=1.282353。本例中，在 5%的显著性

9、水平下，解释变量个数为2,样本容量为21,查表得di=1.22.du =1.42，而 D.W.=1.282353,位于下限与上限之间，不能确定相关性。(4) 拉格朗日乘数(LM )检验法Breusch-Godfrey Serial Correlation LM Test:F-statistic6.662380Probability0.007304Obs*R-squared9.227442Probability0.009915Test Equati on:De pendent Variable: RESIDMethod: Least SquaresDate: 12/26/09 Time: 22:

10、55Presa mple miss ing value lagged residuals set to zero.VariableCoefficie ntStd. Error t-StatisticProb.C-35.61516236.2598-0.1507460.8820X0.0055200.0154080.3582450.7246RESID(-1)0.5780690.1953062.9598070.0088RESID(-2)-0.6179980.200927-3.0757290.0069R-squared0.439402Mean dependent var1.53E-12Adjusted

11、R-squared0.340473S.D. dependent var927.2503S.E. of regressi on753.0318Akaike info criteri on16.25574Sum squared resid9639967.Schwarz criteri on16.45469Log likelihood-166.6852F-statistic4.441587Durbi n- Watson stat2.569721Prob(F-statistic)0.017675由上表可知：含二阶滞后残差项的辅助回归为:et =-35.61516+0.05520X+0.578069e-

12、1 0.617998.2(-0.1507) (0.3582)(2.9598)(-3.0757)R2 =0.439402于是，LM=19 X 0.439402=8.348638，该值大于显著性水平为 5%自由度为2的X 2的临界值X 2.05 2 =5.991 ,由此判断原模型存在2阶序列相关性。三、序列相关的补救(1)广义差分法估计模型由D.W.=1.282353,得到一阶自相关系数的估计值p=1-DW/2=0.6412则 DY=Y-0.6412*Y(-1)， DX=X-0.6412*X(-1)；以 DY 为因变量，DX为解释变量，用OLS法做回归模型，这样就生成了经过广义差分后的模型。Dep

13、endent Variable: DYMethod: Least SquaresDate: Uf22f03 Time; 09-25SatTiple(atljusted): 1931 2000Included observations; 2D after adjusting end卩oinlsVariableCoefficientSid. Errort-StatisticProb.C282.1545321.67610.8771380.3920DX1J712140 04G61225.12692QQDOOR-squared0.972280Mean dep endent var6346747Adjus

14、ted R-squared0.970741Sr. dependemt var5559 J45S E of regression951.Q1B9Akaike info criterionIB 64753Sum squared resid1B279796Schwarz criterion1B74715Lug likelihood-164.4758F-sltislicE3r3B21Durbin-Walson stat1.751259P rob(F-statisticD.DDaDDQ由上表知D.W.=1.751259,在5%的显著性水平下，解释变量个数为2,样本容量为20,查表得di=1.20, du

15、=1.41,而D.W.=1.751259,大于上限du=1.41,可知模型经过广义差分后不存在相关性。(2)科克伦-奥科特法估计模型Dep endent Variable; Method: Least SquaresDate: 12Z229 Time; 09:33SamplA(adjusted): 1931 2000Included observations: 20 after adjusting end pointsConvergente achieved after 5 iterationsVariableCoefficientStd. Errort-StatisticCBE3.537748524731.367432 1893X1 180S42J2BaO540.93669CLimoAR(103573880.2260211.5834310.1317R-squared3 995405Mean dep endent var14331 47Adjusted R-squred0.994364S.D. dependent var13079,93S.E. of regression937.3403Akaike info criterion16.66145Sum squared resid14936316Sc