计量经济学自相关性检验报告分

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：丫二；其中，X表示全社会固定资产投资，Y表示工业增加值。下表列出了中国1998-2000的全社会固定资产投资X与工业增加值丫的统计数据。单位：亿元年份固定资产投资X工业增加值Y年份固定资产投资X工业增加值Y：1980910.91996.519915594.58087.119819612048.419928080.110284.519821230.42162.3199313072.314143.819831430.12375.619941704

2、2.119359.619841832.92789199520019.324718.319852543.23448.7199622913.529082.619863120.63967199724941.132412.119873791.74585.8199828406.233387.919884753.85777.2199929854.735087.219894410.46484200032917.739570.3199045176858、估计回归方程Dependent Variable: YMethod: Least SquaresDate: 12/22/09 Time: 08:53Sampl

3、e: 1980 2000Included observations: 21VariableCoefficientStd. Error t-StatisticProb.C668 0114298 16732.2403920.0372X1.1818610 01934461.096300 0000R-squared0.994936Mean dependent var13744.09Adjusted R-squared0.994669S.D. dependent var13029.80S E. of regression951 3388Akaike info criterion16.64401Sum s

4、quared resid17195864Schwarz criterion16.74349Log likelihood-1727621F-statistic3732.768Durbin-Watson stat1.282353Prob(F-statistic)0 000000OLS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。

5、(2) 回归检验法一阶回归检验Dependent Varible: EMethod: Least SquaresDate: 12Z22/09 Time: 09:41Sample(adjusted): 1981 2DDDIncluded observations: 20 after adjusting endpointsVariableCoefficientStd. Errort*StatisticProb.E(-1)D. 356978 213B461 BS932D0.1114R-squaredAdjusted R-squared S.E. of regression Sum s q u a r

6、e d resid Log likelihood1277440.127744886.776114941067 -163.6177Mean dependent var S.D. dependent var Akaike imfo 匚riterioriSchwarz criterion Durbin-Watsori stat-12.59658949.493516.4617716.511561.5B27B6et=0.356978et_i + e t二阶回归检验Dependent Variable: EMethod: Least SquaresDate: 12/22/09 Time: 09:41Sam

7、ple(adjusted): 1982 2000Included observations: 19 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb.E(-1)0 572433OJ955872.9267460.0094E(-2)0.6078310.1996163.0450030.0073R-squared0.434191Mean dependent var-26.13432Adjusted R-squared0.400908S.D. dependent var973 52b7S E of regressi

8、on753.5196Akaike info criterion16 18669Sum squared resid9652459.Schwarz criterion16.28610Log likelihood-151 7735Durbin-Watson stat2.530763et =0.572433et-1 0.607831et-2 + e 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,

9、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:Depe ndent Variable: RESIDMethod: Least SquaresDate: 12/26/09 Time: 22:55Presample miss ing value lagged residuals set to zero.V

10、ariableCoefficient Std. Error t-Statistic Prob.-35.61516 236.2598-0.1507460.8820X0.0055200.0154080.3582450.7246RESID(-1)0.5780690.1953062.9598070.0088RESID(-2)-0.6179980.200927-3.0757290.0069R-squared0.439402Mean depe ndent var1.53E-12Adjusted R-squared0.340473S.D. dependent var927.2503S.E. of regre

11、ssi 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-i 0.6179982(-0.1507) (0.3582)(2.9598)(-3.0757)R2 =0.43940

12、2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。Dependent Variable: DYMethod： Least SquaresDate: 12/2

13、2/09 Time: 09:25Sample (adj listed): 1981 2000Included obsen/ations: 20 after adjusting endpointsVariableCoefficientStd Error(-StatisticProbC282.1545321.67610.8771390.3920DX1.1712140.04661225.126920.0000R-squared0.972280Mean dependent var6346747Adjusted R-squared0.970741S.D. dependent var5559745S.E.

14、 of regression951.0169Akaike info criterion16.64758Sum squared resid16279796Schwarz criterion16,74715Log likelihood-164.4758statistic631.3621Durbin-Watson stat1751259Prob(F-statistic)0.000000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=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

15、存在相关性。(2)科克伦-奥科特法估计模型Dependent Variable: YMethod: Least SquaresDate: 12/22>09 Time: 09:38Sample(adjusted)： 1981 2000Included observations: 20 after adjusting endpointsConvergence achieved after 5 iterationsVariableCoefficientStd. ErrorV StatisticProb.C663.5377485,24731.3674220,1893X1.1906420,02830540.986690.0000阳0.3578880,2260211.5834310,1317R-squared0.995405Mean dependent var14331.47Adjusted R-squared0.994864S.D. dependent var13079.93S,E, of regression937.3403Akaike info criterion16.66145Sum squared resid14936316Schwar