Проверка на коинтеграцию:
Используем метод Ингла-Грейнжера, оченим уравнение:
ln ftt=αln micext+c+εt
ln ftt=1,72 ln micext+2943,312
Dependent Variable: FT |
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Method: Least Squares |
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Date: 11/30/11 Time: 22:20 |
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Sample: 2008M07 2011M10 |
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Included observations: 40 |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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MICEX |
1.716453 |
0.095313 |
18.00856 |
0.0000 |
C |
2943.312 |
127.7643 |
23.03704 |
0.0000 |
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R-squared |
0.895117 |
Mean dependent var |
5168.314 |
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Adjusted R-squared |
0.892357 |
S.D. dependent var |
627.1660 |
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S.E. of regression |
205.7670 |
Akaike info criterion |
13.54007 |
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Sum squared resid |
1608922. |
Schwarz criterion |
13.62452 |
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Log likelihood |
-268.8015 |
Hannan-Quinn criter. |
13.57061 |
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F-statistic |
324.3082 |
Durbin-Watson stat |
0.874584 |
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Prob(F-statistic) |
0.000000 |
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Создаем остатки и оцениваем модель: ∆ e(t) = βe(t-1) + α ∆ e(t-1) + εt
Для этого в командной строке вводим: ls d(e) e(-1) c @trend
Dependent Variable: D(E) |
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Method: Least Squares |
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Date: 11/30/11 Time: 22:22 |
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Sample (adjusted): 2008M08 2011M10 |
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Included observations: 39 after adjustments |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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E(-1) |
-0.446219 |
0.138258 |
-3.227430 |
0.0027 |
C |
23.83186 |
57.07848 |
0.417528 |
0.6788 |
@TREND |
-1.019548 |
2.491758 |
-0.409168 |
0.6848 |
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R-squared |
0.224459 |
Mean dependent var |
4.187186 |
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Adjusted R-squared |
0.181373 |
S.D. dependent var |
192.3849 |
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S.E. of regression |
174.0661 |
Akaike info criterion |
13.23055 |
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Sum squared resid |
1090764. |
Schwarz criterion |
13.35852 |
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Log likelihood |
-254.9957 |
Hannan-Quinn criter. |
13.27646 |
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F-statistic |
5.209593 |
Durbin-Watson stat |
1.507279 |
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Prob(F-statistic) |
0.010301 |
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с и trend убираем, так как они не значимы
Dependent Variable: D(E) |
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Method: Least Squares |
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Date: 11/30/11 Time: 22:23 |
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Sample (adjusted): 2008M08 2011M10 |
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Included observations: 39 after adjustments |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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E(-1) |
-0.440123 |
0.134085 |
-3.282416 |
0.0022 |
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R-squared |
0.220522 |
Mean dependent var |
4.187186 |
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Adjusted R-squared |
0.220522 |
S.D. dependent var |
192.3849 |
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S.E. of regression |
169.8529 |
Akaike info criterion |
13.13305 |
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Sum squared resid |
1096301. |
Schwarz criterion |
13.17571 |
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Log likelihood |
-255.0945 |
Hannan-Quinn criter. |
13.14835 |
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Durbin-Watson stat |
1.509029 |
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Получаем уравнение: ∆ ln et= -0.440123ln et-1 +εt
Проверим остатки на автокорреляцию:
Breusch-Godfrey Serial Correlation LM Test: |
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F-statistic |
2.669544 |
Prob. F(5,33) |
0.0392 |
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Obs*R-squared |
11.21987 |
Prob. Chi-Square(5) |
0.0472 |
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Test Equation: |
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Dependent Variable: RESID |
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Method: Least Squares |
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Date: 11/30/11 Time: 22:23 |
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Sample: 2008M08 2011M10 |
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Included observations: 39 |
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Presample missing value lagged residuals set to zero. |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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E(-1) |
-4.010100 |
1.224846 |
-3.273964 |
0.0025 |
RESID(-1) |
4.009770 |
1.183404 |
3.388335 |
0.0018 |
RESID(-2) |
2.081897 |
0.684788 |
3.040205 |
0.0046 |
RESID(-3) |
1.096487 |
0.397316 |
2.759733 |
0.0094 |
RESID(-4) |
0.692142 |
0.251502 |
2.752031 |
0.0095 |
RESID(-5) |
0.270469 |
0.196545 |
1.376116 |
0.1781 |
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R-squared |
0.287689 |
Mean dependent var |
3.451105 |
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Adjusted R-squared |
0.179763 |
S.D. dependent var |
169.8170 |
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S.E. of regression |
153.7980 |
Akaike info criterion |
13.04980 |
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Sum squared resid |
780576.3 |
Schwarz criterion |
13.30573 |
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Log likelihood |
-248.4710 |
Hannan-Quinn criter. |
13.14162 |
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Durbin-Watson stat |
1.832194 |
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Автокорреляция есть,тогда добавим лаг d(e(-1))
Dependent Variable: D(E) |
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Method: Least Squares |
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Date: 11/30/11 Time: 22:37 |
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Sample (adjusted): 2008M09 2011M10 |
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Included observations: 38 after adjustments |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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E(-1) |
-0.510924 |
0.137829 |
-3.706949 |
0.0007 |
D(E(-1)) |
0.226450 |
0.149473 |
1.514988 |
0.0385 |
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R-squared |
0.275533 |
Mean dependent var |
-8.229094 |
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Adjusted R-squared |
0.255409 |
S.D. dependent var |
178.4304 |
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S.E. of regression |
153.9670 |
Akaike info criterion |
12.96255 |
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Sum squared resid |
853410.5 |
Schwarz criterion |
13.04874 |
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Log likelihood |
-244.2885 |
Hannan-Quinn criter. |
12.99322 |
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Durbin-Watson stat |
1.907193 |
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Все коэффициенты значимы
Проверим на автокорреляцию:
Breusch-Godfrey Serial Correlation LM Test: |
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F-statistic |
1.149110 |
Prob. F(5,31) |
0.3560 |
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Obs*R-squared |
5.862999 |
Prob. Chi-Square(5) |
0.3198 |
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Test Equation: |
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Dependent Variable: RESID |
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Method: Least Squares |
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Date: 11/30/11 Time: 22:38 |
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Sample: 2008M09 2011M10 |
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Included observations: 38 |
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Presample missing value lagged residuals set to zero. |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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E(-1) |
0.535253 |
0.357357 |
1.497810 |
0.1443 |
D(E(-1)) |
-0.680532 |
0.339995 |
-2.001593 |
0.0541 |
RESID(-1) |
0.122899 |
0.376286 |
0.326611 |
0.7462 |
RESID(-2) |
-0.615732 |
0.356632 |
-1.726518 |
0.0942 |
RESID(-3) |
-0.616962 |
0.272869 |
-2.261015 |
0.0309 |
RESID(-4) |
-0.273541 |
0.195629 |
-1.398264 |
0.1720 |
RESID(-5) |
-0.047678 |
0.174593 |
-0.273082 |
0.7866 |
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R-squared |
0.154289 |
Mean dependent var |
-7.415814 |
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Adjusted R-squared |
-0.009396 |
S.D. dependent var |
151.6861 |
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S.E. of regression |
152.3971 |
Akaike info criterion |
13.05568 |
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Sum squared resid |
719970.9 |
Schwarz criterion |
13.35734 |
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Log likelihood |
-241.0579 |
Hannan-Quinn criter. |
13.16301 |
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Durbin-Watson stat |
2.098437 |
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Автокорреляции нет, так как pob>0,05
Variable |
Coefficient |
Std. Error |
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E(-1) |
-0.510924 |
0.137829 |
D(E(-1)) |
0.226450 |
0.149473 |
∆ln et=-0.510924ln et-1 + 0.226450∆ln et-1 +εt
Проверим гипотезу:
H0: ρ=0, ряд et принадлежит классу DS, и коинтеграции нет.
H1: ρ<0, ряд et принадлежит классу TS, и коинтеграции есть.
Dependent Variable: D(E) |
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Method: Least Squares |
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Date: 11/30/11 Time: 22:39 |
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Sample (adjusted): 2008M09 2011M10 |
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Included observations: 38 after adjustments |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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E(-1) |
-0.510924 |
0.137829 |
-3.706949 |
0.0007 |
D(E(-1)) |
0.226450 |
0.149473 |
1.514988 |
0.0385 |
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R-squared |
0.275533 |
Mean dependent var |
-8.229094 |
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Adjusted R-squared |
0.255409 |
S.D. dependent var |
178.4304 |
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S.E. of regression |
153.9670 |
Akaike info criterion |
12.96255 |
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Sum squared resid |
853410.5 |
Schwarz criterion |
13.04874 |
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Log likelihood |
-244.2885 |
Hannan-Quinn criter. |
12.99322 |
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Durbin-Watson stat |
1.907193 |
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Асимптотические критические значения для ADF
Число переменных (всех) |
Размер выборки |
Уровень значимости |
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1% |
5% |
10% |
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2 |
50 |
-4,32 |
-3,67 |
-3,28 |
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100 |
-4,07 |
-3,37 |
-3,03 |
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200 |
-4,00 |
-3,37 |
-3,02 |
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асимпт |
-3.90 |
-3.34 |
-3.04 |
tstat=-3.7 <tcr = -3,67, значит ряды коинтегрированны.
Коинтегрирующий вектор: (1, -1.716453)