三、模型的估计和检验:
1)平稳性检验:单位根检验
Lny ADF 一阶差分 只有截距项 滞后3阶
ADF Test Statistic -2.807303 1% Critical Value* -3.7856
5% Critical Value -3.0114
10% Critical Value -2.6457
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LNY,2)
Method: Least Squares
Date: 06/14/05 Time: 10:15
Sample(adjusted): 1983 2003
Included observations: 21 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(LNY(-1)) -0.581207 0.207034 -2.807303 0.0126
D(LNY(-1),2) 0.597357 0.218600 2.732652 0.0148
D(LNY(-2),2) 0.018730 0.222544 0.084165 0.9340
D(LNY(-3),2) 0.293551 0.207049 1.417785 0.1754
C 0.090017 0.033464 2.689959 0.0161
R-squared 0.446263 Mean dependent var 0.004307
Adjusted R-squared 0.307828 S.D. dependent var 0.066967
S.E. of regression 0.055715 Akaike info criterion -2.732888
Sum squared resid 0.049666 Schwarz criterion -2.484192
Log likelihood 33.69532 F-statistic 3.223642
Durbin-Watson stat 1.883066 Prob(F-statistic) 0.040398
以10%的标准LNY不存在单位根,一阶差分平稳。
LNK ADF 一阶差分 只有截距项 滞后3阶
ADF Test Statistic -3.012373 1% Critical Value* -3.7856
5% Critical Value -3.0114
10% Critical Value -2.6457
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LNK,2)
Method: Least Squares
Date: 06/14/05 Time: 10:19
Sample(adjusted): 1983 2003
Included observations: 21 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(LNK(-1)) -0.898176 0.298162 -3.012373 0.0083
D(LNK(-1),2) 0.404224 0.258497 1.563749 0.1374
D(LNK(-2),2) 0.282612 0.240281 1.176175 0.2567
D(LNK(-3),2) 0.310454 0.227736 1.363218 0.1917
C 0.141537 0.049395 2.865403 0.0112
R-squared 0.380186 Mean dependent var 0.004144
Adjusted R-squared 0.225232 S.D. dependent var 0.102694
S.E. of regression 0.090392 Akaike info criterion -1.765057
Sum squared resid 0.130733 Schwarz criterion -1.516361
Log likelihood 23.53309 F-statistic 2.453546
Durbin-Watson stat 2.004426 Prob(F-statistic) 0.088031
以5%的标准,没有单位根,一阶差分平稳。
LNL ADF只有截距项和趋势 滞后1阶一阶差分
ADF Test Statistic -3.628678 1% Critical Value* -4.4167
5% Critical Value -3.6219
10% Critical Value -3.2474
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LNL,2)
Method: Least Squares
Date: 06/14/05 Time: 10:22
Sample(adjusted): 1981 2003
Included observations: 23 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(LNL(-1)) -1.303252 0.359153 -3.628678 0.0018
D(LNL(-1),2) 0.019683 0.227961 0.086346 0.9321
C 0.105447 0.033455 3.151939 0.0052
@TREND(1978) -0.004507 0.001580 -2.852753 0.0102
R-squared 0.632964 Mean dependent var -0.002063
Adjusted R-squared 0.575011 S.D. dependent var 0.051344
S.E. of regression 0.033472 Akaike info criterion -3.799468
Sum squared resid 0.021287 Schwarz criterion -3.601991
Log likelihood 47.69389 F-statistic 10.92201
Durbin-Watson stat 1.991014 Prob(F-statistic) 0.000216
以5%的标准,没有单位根,一阶差分平稳
LNE(-2) ADF 有趋势和截距项 滞后1阶一阶差分
ADF Test Statistic -4.419992 1% Critical Value* -4.4415
5% Critical Value -3.6330
10% Critical Value -3.2535
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LNE1,2)
Method: Least Squares
Date: 06/14/05 Time: 11:28
Sample(adjusted): 1982 2003
Included observations: 22 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(LNE1(-1)) -1.577432 0.356886 -4.419992 0.0003
D(LNE1(-1),2) 0.205990 0.219247 0.939531 0.3599
C 0.018412 0.035967 0.511912 0.6149
@TREND(1978) -0.001323 0.002272 -0.582098 0.5677
R-squared 0.702869 Mean dependent var 0.001932
Adjusted R-squared 0.653348 S.D. dependent var 0.113284
S.E. of regression 0.066698 Akaike info criterion -2.414312
Sum squared resid 0.080076 Schwarz criterion -2.215940
Log likelihood 30.55743 F-statistic 14.19315
Durbin-Watson stat 2.064102 Prob(F-statistic) 0.000054
以5%的标准,没有单位根,一阶差分平稳
综上,模型中的变量都是一阶差分平稳。对变量进行回归LS LNY C LNK LNL LNE(-2)
Dependent Variable: LNY
Method: Least Squares
Date: 06/14/05 Time: 11:31
Sample(adjusted): 1980 2003
Included observations: 24 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C 3.612380 1.046778 3.450951 0.0025
LNK 0.920368 0.075645 12.16690 0.0000
LNL -0.387481 0.141687 -2.734767 0.0128
LNE(-2) 0.164260 0.067373 2.438081 0.0242
R-squared 0.998259 Mean dependent var 9.374063
Adjusted R-squared 0.997998 S.D. dependent var 1.164977
S.E. of regression 0.052123 Akaike info criterion -2.919421
Sum squared resid 0.054336 Schwarz criterion -2.723078
Log likelihood 39.03305 F-statistic 3823.231
Durbin-Watson stat 0.654112 Prob(F-statistic) 0.000000
R2=0.998259 拟合程度很好, F=3823.231 通过了F检验,模型设定正确。
回归结果,得:
LNY=3.612380 +0.920368LNK—0.387481LNL+0.164260LNE(-2)
(各参数均通过T检验)
对残差项进行平稳性检验,单位根检验
0阶,没有趋势和截距,滞后一阶
ADF Test Statistic -2.108609 1% Critical Value* -2.6756
5% Critical Value -1.9574
10% Critical Value -1.6238
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(R2)
Method: Least Squares
Date: 06/14/05 Time: 11:34
Sample(adjusted): 1982 2003
Included observations: 22 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
R2(-1) -0.460598 0.218437 -2.108609 0.0478
D(R2(-1)) 0.260993 0.238624 1.093744 0.2871
R-squared 0.146646 Mean dependent var -0.008221
Adjusted R-squared 0.103978 S.D. dependent var 0.040171
S.E. of regression 0.038026 Akaike info criterion -3.614601
Sum squared resid 0.028919 Schwarz criterion -3.515415
Log likelihood 41.76061 F-statistic 3.436934
Durbin-Watson stat 1.816806 Prob(F-statistic) 0.078563
以5%的标准,没有单位根,平稳。说明存在协整。