Durbin-Watson stat
2.020315
由上表可知，对常数的回归结果并不显著。下面得到残差平方的自相关图：
Date: 12/16/14 Time: 08:18 Sample: 1 957
Included observations: 957
Autocorrelation | | |* | | | | | | | | | |* | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Partial Correlation | | |* | | | | | | | | | |* | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
AC PAC Q-Stat Prob 1 0.050 2 0.107 3 0.020 4 0.035 5 0.020 6 0.031 7 0.084 8 0.015 9 0.045 10 0.061 12 0.039 13 0.053
0.050 0.105 0.010 0.023 0.014 0.024 0.078 0.001 0.027 0.054 0.025 0.044
2.3771 13.380 13.769 14.958 15.331 16.271 23.070 23.278 25.212 28.818 28.999 30.492 33.261 33.268 33.269 33.278 33.657 35.450 35.490 36.486 39.334 39.829 40.012 42.216 42.322 42.585 43.014 43.642 44.979 45.797 46.343 47.339 48.765 49.134 49.734
0.123 0.001 0.003 0.005 0.009 0.012 0.002 0.003 0.003 0.001 0.002 0.002 0.002 0.003 0.004 0.007 0.009 0.008 0.012 0.013 0.009 0.011 0.015 0.012 0.017 0.021 0.026 0.030 0.030 0.032 0.038 0.040 0.038 0.045 0.051
11 0.014 -0.003
14 0.003 -0.018 15 -0.001 -0.014 16 -0.003 -0.011 17 0.020 18 0.043 20 0.032 21 0.054 23 0.014 25 0.010
0.010 0.041 0.014 0.052 0.001 0.003
19 0.006 -0.010
22 -0.022 -0.039 24 -0.047 -0.048 26 -0.016 -0.009 27 -0.021 -0.030 28 0.025 30 0.029 31 0.023 32 0.032 34 0.019 35 0.025
0.023 0.019 0.031 0.027 0.022 0.030 - 5 -
29 -0.037 -0.031
33 -0.038 -0.045
| |
| |
36 0.016
0.018
49.984
0.061
图4.4 残差平方的自相关图
由上图可知，残差平方序列在滞后三阶并不异于零，即存在自相关性，进一步进行lm检验，这里选取滞后将阶数为3，检验结果如下：
表4.3 ARCH效应检验结果
Heteroskedasticity Test: ARCH F-statistic
4.373176 Prob. F(3,950)
0.0046 0.0046
Obs*R-squared
12.99530 Prob. Chi-Square(3)
由上表可知，p值为0.0046，因此在1%的显著水平下是存在ARCH效应的。选择滞后阶数更高的进行检
验,发现滞后4阶也满足在1%的显著水平下存在ARCH效应，再选取其他高阶进行检验，发现高阶残差平方项均不满足。
4.3 模型的估计
分别估计ARCH（2）、ARCH（1）和GARCH（1，1），由于R不存在自相关性，而且对常数回归也不显著，因此不对均值方程进行设定，之设定方差方程。AECH（2）估计结果如下：
表4.4 arch（2）模型的估计结果
Dependent Variable: R
Method: ML - ARCH (Marquardt) - Normal distribution Date: 12/16/14 Time: 08:38 Sample: 1 957
Included observations: 957
Convergence achieved after 8 iterations Presample variance: backcast (parameter = 0.7) GARCH = C(1) + C(2)*RESID(-1)^2 + C(3)*RESID(-2)^2
Variable
C RESID(-1)^2 RESID(-2)^2 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient
Std. Error
z-Statistic 18.41652 2.219053 4.432849
Prob. 0.0000 0.0265 0.0000 0.010480 1.292140 3.336256 3.351503 3.342063 - 6 -
Variance Equation 1.409961 0.047531 0.106284
0.076560 0.021420 0.023977
-0.000066 Mean dependent var 0.000979 S.D. dependent var 1.291507 Akaike info criterion 1596.268 Schwarz criterion -1593.399 Hannan-Quinn criter. 2.020182
可以看出，残差平方滞后项的系数在5%的显著水平下都显著，因此选择
arch（2）合适，再选择
ARCH(1)。
表4.5 arch（1）模型的估计结果
Dependent Variable: R
Method: ML - ARCH (Marquardt) - Normal distribution Date: 12/16/14 Time: 08:40 Sample: 1 957
Included observations: 957
Convergence achieved after 7 iterations Presample variance: backcast (parameter = 0.7) GARCH = C(1) + C(2)*RESID(-1)^2
Variable
C RESID(-1)^2 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient
Std. Error
z-Statistic 25.50884 2.090131
Prob. 0.0000 0.0366 0.010480 1.292140 3.350173 3.360337 3.354044
Variance Equation 1.594810 0.043267
0.062520 0.020701
-0.000066 Mean dependent var 0.000979 S.D. dependent var 1.291507 Akaike info criterion 1596.268 Schwarz criterion -1601.058 Hannan-Quinn criter. 2.020182
可以看出，残差平方滞后项的系数在5%的显著水平下显著，因此选择ARCH（1）合适。下面对
GARCH（1，1）进行估计。
表4.6 GARCH（1，1）模型的估计结果
Dependent Variable: R
Method: ML - ARCH (Marquardt) - Normal distribution Date: 12/16/14 Time: 08:42 Sample: 1 957
Included observations: 957
Convergence achieved after 9 iterations Presample variance: backcast (parameter = 0.7) GARCH = C(1) + C(2)*RESID(-1)^2 + C(3)*GARCH(-1)
Variable
C
Coefficient
Std. Error
z-Statistic 2.073026 - 7 -
Prob. 0.0382
Variance Equation 0.046373
0.022370
RESID(-1)^2 GARCH(-1)
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
0.038396 0.934896
0.009194 0.019410
4.176296 48.16515
0.0000 0.0000 0.010480 1.292140 3.326751 3.341998 3.332558
-0.000066 Mean dependent var 0.000979 S.D. dependent var 1.291507 Akaike info criterion 1596.268 Schwarz criterion -1588.850 Hannan-Quinn criter. 2.020182
以上模型的系数均满足非负性，而且在5%的水平下显著。 4.4模型残差的检验
下面进行残差的自相关性的检验，检验结果如下：
Date: 12/16/14 Time: 08:50 Sample: 1 957
Included observations: 957
Autocorrelation | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Partial Correlation | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
AC PAC Q-Stat Prob 1 0.002 2 0.020
0.002 0.020
0.0042 0.3950 0.4260 0.5415 1.1481 3.5743 7.2970 7.3261 7.7988 10.192 10.313 11.926 13.305 14.761 14.832
0.949 0.821 0.935 0.969 0.950 0.734 0.399 0.502 0.555 0.424 0.502 0.452 0.425 0.395 0.464
3 -0.006 -0.006 4 -0.011 -0.011 5 0.025 7 0.062 8 0.005 9 0.022 10 0.050 11 0.011
0.025 0.061 0.007 0.020 0.049 0.014
6 -0.050 -0.050
12 -0.041 -0.048 13 -0.038 -0.031 14 0.039 15 0.009
0.038 0.008
图4.5 ARCH(2)模型残差项的自相关图
Date: 12/16/14 Time: 08:51 Sample: 1 957
Included observations: 957
Autocorrelation
Partial Correlation
AC PAC Q-Stat Prob
- 8 -
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
1 -0.004 -0.004 2 0.032
0.032
3 -0.005 -0.005 4 -0.007 -0.009 5 0.028 7 0.066 8 0.012 9 0.029 10 0.055 11 0.015
0.029 0.064 0.015 0.025 0.054 0.017
6 -0.039 -0.039
0.0190 1.0108 1.0351 1.0887 1.8669 3.3497 7.5614 7.7017 8.5082 11.480 11.699 13.620 14.860 16.013 16.040
0.890 0.603 0.793 0.896 0.867 0.764 0.373 0.463 0.484 0.321 0.387 0.326 0.316 0.313 0.379
12 -0.044 -0.053 13 -0.036 -0.032 14 0.034 15 0.005
0.034 0.005
图4.6 ARCH(1)模型残差项的自相关图
Date: 12/16/14 Time: 08:52 Sample: 1 957
Included observations: 957
Autocorrelation | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Partial Correlation | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
AC PAC Q-Stat Prob 1 0.010 2 0.036
0.010 0.036
0.0894 1.3190 1.3196 1.3196 2.2129 3.8917 7.3928 7.4137 8.0945 11.607 11.786 13.630 14.693 16.088 16.100
0.765 0.517 0.724 0.858 0.819 0.691 0.389 0.493 0.525 0.312 0.380 0.325 0.327 0.308 0.375
3 -0.001 -0.001 4 -0.000 -0.001 5 0.030 7 0.060 8 0.005 9 0.027 10 0.060 11 0.014
0.031 0.059 0.006 0.022 0.059 0.013
6 -0.042 -0.042
12 -0.044 -0.054 13 -0.033 -0.028 14 0.038 15 0.004
0.038 0.003
图4.7 GARCH(1,1)模型残差项的自相关图
观察残差的自相关图，可以看出均不存在自相关性。下面观察残差平方的自相关图。
Date: 12/16/14 Time: 08:53
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