Лабораторная работа №3
Задание 1:
Т. к. все ряды стационарные, значит, строить буду ARMA-модели.
Для исходного ряда а:
Построим коррелограмму:
Sample: 1996:1 2007:1 | ||||||
Included observations: 45 | ||||||
Autocorrelation | Partial Correlation | AC | PAC | Q-Stat | Prob | |
. | . | | . | . | | 1 | -0.023 | -0.023 | 0.0260 | 0.872 |
.*| . | | .*| . | | 2 | -0.101 | -0.101 | 0.5265 | 0.769 |
. | . | | . | . | | 3 | 0.028 | 0.023 | 0.5653 | 0.904 |
. |*. | | . |*. | | 4 | 0.116 | 0.108 | 1.2550 | 0.869 |
. | . | | . | . | | 5 | 0.012 | 0.024 | 1.2632 | 0.939 |
**| . | | **| . | | 6 | -0.288 | -0.273 | 5.7623 | 0.450 |
. | . | | . | . | | 7 | -0.024 | -0.045 | 5.7955 | 0.564 |
. |*. | | . | . | | 8 | 0.096 | 0.043 | 6.3218 | 0.611 |
.*| . | | .*| . | | 9 | -0.068 | -0.060 | 6.5968 | 0.679 |
.*| . | | .*| . | | 10 | -0.148 | -0.096 | 7.9245 | 0.636 |
. | . | | . | . | | 11 | 0.059 | 0.061 | 8.1440 | 0.700 |
. | . | | .*| . | | 12 | 0.039 | -0.062 | 8.2397 | 0.766 |
. | . | | . | . | | 13 | 0.030 | 0.035 | 8.2993 | 0.824 |
.*| . | | .*| . | | 14 | -0.143 | -0.100 | 9.6851 | 0.785 |
. |*. | | . |*. | | 15 | 0.103 | 0.076 | 10.430 | 0.792 |
. | . | | .*| . | | 16 | 0.016 | -0.080 | 10.447 | 0.842 |
. | . | | . | . | | 17 | -0.015 | 0.032 | 10.465 | 0.883 |
.*| . | | .*| . | | 18 | -0.072 | -0.071 | 10.872 | 0.900 |
. | . | | . | . | | 19 | 0.008 | 0.003 | 10.878 | 0.928 |
. | . | | .*| . | | 20 | 0.010 | -0.079 | 10.887 | 0.949 |
Из нее определяем, что p=0, q=0, значит «белый шум».
Для ряда bf:
Построим коррелограмму:
Sample: 1996:1 2007:1 | ||||||
Included observations: 45 | ||||||
Autocorrelation | Partial Correlation | AC | PAC | Q-Stat | Prob | |
. | . | | . | . | | 1 | -0.023 | -0.023 | 0.0260 | 0.872 |
.*| . | | .*| . | | 2 | -0.101 | -0.101 | 0.5265 | 0.769 |
. | . | | . | . | | 3 | 0.028 | 0.023 | 0.5653 | 0.904 |
. |*. | | . |*. | | 4 | 0.116 | 0.108 | 1.2550 | 0.869 |
. | . | | . | . | | 5 | 0.012 | 0.024 | 1.2632 | 0.939 |
**| . | | **| . | | 6 | -0.288 | -0.273 | 5.7623 | 0.450 |
. | . | | . | . | | 7 | -0.024 | -0.045 | 5.7955 | 0.564 |
. |*. | | . | . | | 8 | 0.096 | 0.043 | 6.3218 | 0.611 |
.*| . | | .*| . | | 9 | -0.068 | -0.060 | 6.5968 | 0.679 |
.*| . | | .*| . | | 10 | -0.148 | -0.096 | 7.9245 | 0.636 |
. | . | | . | . | | 11 | 0.059 | 0.061 | 8.1440 | 0.700 |
. | . | | .*| . | | 12 | 0.039 | -0.062 | 8.2397 | 0.766 |
. | . | | . | . | | 13 | 0.030 | 0.035 | 8.2993 | 0.824 |
.*| . | | .*| . | | 14 | -0.143 | -0.100 | 9.6851 | 0.785 |
. |*. | | . |*. | | 15 | 0.103 | 0.076 | 10.430 | 0.792 |
. | . | | .*| . | | 16 | 0.016 | -0.080 | 10.447 | 0.842 |
. | . | | . | . | | 17 | -0.015 | 0.032 | 10.465 | 0.883 |
.*| . | | .*| . | | 18 | -0.072 | -0.071 | 10.872 | 0.900 |
. | . | | . | . | | 19 | 0.008 | 0.003 | 10.878 | 0.928 |
. | . | | .*| . | | 20 | 0.010 | -0.079 | 10.887 | 0.949 |
Из нее определяем, что p=0, q=0, значит «белый шум».
Для ряда cf:
Построим коррелограмму:
Sample: 1996:1 2007:1 | ||||||
Included observations: 44 | ||||||
Autocorrelation | Partial Correlation | AC | PAC | Q-Stat | Prob | |
. | . | | . | . | | 1 | -0.020 | -0.020 | 0.0180 | 0.893 |
. | . | | . | . | | 2 | -0.054 | -0.054 | 0.1565 | 0.925 |
. | . | | . | . | | 3 | -0.009 | -0.011 | 0.1608 | 0.984 |
. | . | | . | . | | 4 | -0.044 | -0.047 | 0.2580 | 0.992 |
. | . | | . | . | | 5 | 0.027 | 0.024 | 0.2958 | 0.998 |
**| . | | **| . | | 6 | -0.227 | -0.233 | 3.0476 | 0.803 |
. |*. | | . |*. | | 7 | 0.099 | 0.099 | 3.5873 | 0.826 |
.*| . | | .*| . | | 8 | -0.095 | -0.133 | 4.0899 | 0.849 |
. | . | | . | . | | 9 | -0.008 | 0.007 | 4.0934 | 0.905 |
. | . | | . | . | | 10 | 0.021 | -0.022 | 4.1200 | 0.942 |
.*| . | | . | . | | 11 | -0.072 | -0.055 | 4.4355 | 0.955 |
. |*. | | . |*. | | 12 | 0.151 | 0.090 | 5.8862 | 0.922 |
. |*. | | . |*. | | 13 | 0.096 | 0.144 | 6.4873 | 0.927 |
. | . | | .*| . | | 14 | -0.030 | -0.084 | 6.5497 | 0.951 |
. | . | | . | . | | 15 | -0.043 | -0.003 | 6.6765 | 0.966 |
. | . | | . | . | | 16 | 0.044 | 0.048 | 6.8149 | 0.977 |
.*| . | | .*| . | | 17 | -0.063 | -0.106 | 7.1108 | 0.982 |
**| . | | **| . | | 18 | -0.235 | -0.190 | 11.402 | 0.877 |
. | . | | . | . | | 19 | -0.048 | -0.045 | 11.588 | 0.902 |
. | . | | .*| . | | 20 | -0.057 | -0.130 | 11.857 | 0.921 |
Из нее определяем, что p=0, q=0, значит «белый шум».
Для ряда df:
Построим коррелограмму:
Sample: 1996:1 2007:1 | ||||||
Included observations: 41 | ||||||
Autocorrelation | Partial Correlation | AC | PAC | Q-Stat | Prob | |
.*| . | | .*| . | | 1 | -0.118 | -0.118 | 0.6136 | 0.433 |
.*| . | | .*| . | | 2 | -0.076 | -0.092 | 0.8773 | 0.645 |
.*| . | | .*| . | | 3 | -0.059 | -0.081 | 1.0371 | 0.792 |
. | . | | . | . | | 4 | 0.005 | -0.021 | 1.0382 | 0.904 |
. |*. | | . |*. | | 5 | 0.109 | 0.097 | 1.6160 | 0.899 |
.*| . | | .*| . | | 6 | -0.175 | -0.159 | 3.1586 | 0.789 |
. |*. | | . |*. | | 7 | 0.115 | 0.096 | 3.8407 | 0.798 |
. | . | | . | . | | 8 | -0.031 | -0.025 | 3.8917 | 0.867 |
.*| . | | .*| . | | 9 | -0.095 | -0.111 | 4.3872 | 0.884 |
.*| . | | .*| . | | 10 | -0.065 | -0.095 | 4.6289 | 0.915 |
.*| . | | .*| . | | 11 | -0.064 | -0.079 | 4.8693 | 0.937 |
. | . | | .*| . | | 12 | 0.010 | -0.091 | 4.8755 | 0.962 |
. |*. | | . |*. | | 13 | 0.071 | 0.082 | 5.1956 | 0.971 |
.*| . | | .*| . | | 14 | -0.157 | -0.178 | 6.8105 | 0.942 |
. |** | | . |** | | 15 | 0.268 | 0.266 | 11.692 | 0.702 |
. | . | | . | . | | 16 | 0.015 | 0.052 | 11.708 | 0.764 |
.*| . | | . | . | | 17 | -0.061 | -0.037 | 11.977 | 0.802 |
.*| . | | .*| . | | 18 | -0.096 | -0.105 | 12.688 | 0.810 |
.*| . | | .*| . | | 19 | -0.079 | -0.081 | 13.190 | 0.829 |
. |** | | . | . | | 20 | 0.200 | 0.016 | 16.558 | 0.681 |
Из нее определяем, что p=0, q=0, значит «белый шум».
Для ряда ef:
Построим коррелограмму:
Sample: 1996:1 2007:1 | ||||||
Included observations: 41 | ||||||
Autocorrelation | Partial Correlation | AC | PAC | Q-Stat | Prob | |
.*| . | | .*| . | | 1 | -0.082 | -0.082 | 0.2991 | 0.584 |
. |*. | | . |*. | | 2 | 0.126 | 0.120 | 1.0146 | 0.602 |
. | . | | . | . | | 3 | -0.055 | -0.037 | 1.1548 | 0.764 |
.*| . | | .*| . | | 4 | -0.081 | -0.105 | 1.4703 | 0.832 |
. |*. | | . |*. | | 5 | 0.080 | 0.081 | 1.7822 | 0.878 |
**| . | | **| . | | 6 | -0.215 | -0.190 | 4.1090 | 0.662 |
. |*. | | . | . | | 7 | 0.093 | 0.043 | 4.5607 | 0.713 |
. | . | | . | . | | 8 | -0.033 | 0.026 | 4.6203 | 0.797 |
. | . | | .*| . | | 9 | -0.028 | -0.061 | 4.6628 | 0.863 |
. | . | | . | . | | 10 | 0.050 | 0.022 | 4.8045 | 0.904 |
. | . | | . | . | | 11 | -0.052 | 0.000 | 4.9624 | 0.933 |
. |*. | | . |*. | | 12 | 0.156 | 0.096 | 6.4396 | 0.892 |
.*| . | | .*| . | | 13 | -0.170 | -0.139 | 8.2559 | 0.827 |
. | . | | . | . | | 14 | -0.009 | -0.053 | 8.2616 | 0.875 |
**| . | | **| . | | 15 | -0.255 | -0.257 | 12.662 | 0.628 |
.*| . | | .*| . | | 16 | -0.108 | -0.124 | 13.483 | 0.637 |
. | . | | . | . | | 17 | -0.016 | -0.034 | 13.501 | 0.702 |
.*| . | | .*| . | | 18 | -0.136 | -0.112 | 14.917 | 0.668 |
. |*. | | . | . | | 19 | 0.127 | 0.011 | 16.206 | 0.643 |
. | . | | . |*. | | 20 | 0.032 | 0.083 | 16.291 | 0.698 |
Из нее определяем, что p=0, q=0, значит «белый шум».
Задание 3:
Построим прогноз исходного ряда а.
Полученная модель выглядит следующим образом.
Dependent Variable: A | ||||
Method: Least Squares | ||||
Sample: 1996:1 2007:1 | ||||
Included observations: 45 | ||||
Variable | Coefficient | Std. Error | t-Statistic | Prob. |
C | -47.56773 | 34.23575 | -1.389417 | 0.1719 |
@TREND() | 1.876614 | 1.340091 | 1.400363 | 0.1686 |
R-squared | 0.043616 | Mean dependent var | -6.282222 | |
Adjusted R-squared | 0.021374 | S. D. dependent var | 118.0176 | |
S. E. of regression | 116.7495 | Akaike info criterion | 12.40136 | |
Sum squared resid | 586109.3 | Schwarz criterion | 12.48166 | |
Log likelihood | -277.0307 | F-statistic | 1.961018 | |
Durbin-Watson stat | 2.059422 | Prob(F-statistic) | 0.168579 |
Так как ARMA-модели нет и все переменные незначимы, то построить прогноз невозможно.
