2 平稳性检验:
首先对X序列进行平稳性分析:
ADF Test Statistic 1.548458 1% Critical Value* -4.1366
5% Critical Value -3.1483
10% Critical Value -2.7180
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(X)
Method: Least Squares
Date: 06/08/05 Time: 00:14
Sample(adjusted): 1992 2003
Included observations: 12 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
X(-1) 0.120312 0.077698 1.548458 0.1559
D(X(-1)) 0.653492 0.534598 1.222401 0.2526
C -11.94777 15.68186 -0.761885 0.4656
R-squared 0.689356 Mean dependent var 51.45250
Adjusted R-squared 0.620324 S.D. dependent var 36.11654
S.E. of regression 22.25424 Akaike info criterion 9.255260
Sum squared resid 4457.259 Schwarz criterion 9.376486
Log likelihood -52.53156 F-statistic 9.986035
Durbin-Watson stat 1.805152 Prob(F-statistic) 0.005190
ADF Test Statistic的值为1.548458,小于临界值,接受原假设,序列是非平稳的。
再对Y序列进行平稳性分析:
ADF Test Statistic -0.291919 1% Critical Value* -4.1366
5% Critical Value -3.1483
10% Critical Value -2.7180
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(Y)
Method: Least Squares
Date: 06/08/05 Time: 00:22
Sample(adjusted): 1992 2003
Included observations: 12 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
Y(-1) -0.008203 0.028102 -0.291919 0.7770
D(Y(-1)) 0.613280 0.263535 2.327126 0.0450
C 4077.591 2647.082 1.540410 0.1578
R-squared 0.376258 Mean dependent var 7969.508
Adjusted R-squared 0.237648 S.D. dependent var 2954.351
S.E. of regression 2579.525 Akaike info criterion 18.76092
Sum squared resid 59885530 Schwarz criterion 18.88214
Log likelihood -109.5655 F-statistic 2.714520
Durbin-Watson stat 1.030166 Prob(F-statistic) 0.119543
ADF Test Statistic的绝对值为0.291919,仍然小于临界值,接受原假设,序列是非平稳的。在经济领域中,我们所得到的时间序列观测值大都不是有平稳过程产生的。此模型中,GDP在大多情况下随时间的位移而持续增长。
3 多重共线性检验:
因为我们建立的模型只有一个解释变量,所以不存在多重共线性
4 异方差检验:
运用ARCH检验:
ARCH Test:
F-statistic 0.020272 Probability 0.889355
Obs*R-squared 0.023914 Probability 0.877105
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 06/07/05 Time: 19:57
Sample(adjusted): 1991 2003
Included observations: 13 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C 68774168 32841075 2.094151 0.0602
RESID^2(-1) -0.071419 0.501610 -0.142379 0.8894
R-squared 0.001840 Mean dependent var 64915836
Adjusted R-squared -0.088902 S.D. dependent var 64101963
S.E. of regression 66890709 Akaike info criterion 39.01566
Sum squared resid 4.92E+16 Schwarz criterion 39.10257
Log likelihood -251.6018 F-statistic 0.020272
Durbin-Watson stat 1.447326 Prob(F-statistic) 0.889355
从输出的辅助回归函数中得obs*-squared为0.023914,在显著性水平为0.05的情况下查卡方分布表得临界..05914.9.87 280.15 .05914.9.值3.84146,由于0.023914<3.84146,并且p值为0.877105〉0.2所以接受原假设,表明模型中随机误差项不存在异方差。