Đồ thị chuỗi TL .000 .002 .004 .006 .008 .010 .012 .014 10 20 30 40 50 60 TL
Sử dụng phần mền Eviews để ước lượng các mô hình, ta đưa ra bảng kết quả sau đây.
Bảng 1
ADF Test Statistic -8.935567 1% Critical Value* -3.5417 5% Critical Value -2.9101 10% Critical Value -2.5923 *MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(TL)
Method: Least Squares Date: 06/07/07 Time: 14:43 Sample(adjusted): 2 61
Included observations: 60 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob. TL(-1) -1.136646 0.127205 -8.935567 0.0000 C 0.007052 0.000930 7.583730 0.0000 R-squared 0.579236 Mean dependent var -0.000110 Adjusted R-squared 0.571981 S.D. dependent var 0.005582 S.E. of regression 0.003652 Akaike info criterion -8.354350 Sum squared resid 0.000774 Schwarz criterion -8.284539 Log likelihood 252.6305 F-statistic 79.84435 Durbin-Watson stat 1.932151 Prob(F-statistic) 0.000000
Bảng 2
Dependent Variable: TL Method: Least Squares Date: 06/07/07 Time: 14:48 Sample(adjusted): 5 61
Included observations: 57 after adjusting endpoints Convergence achieved after 14 iterations
Backcast: 1 4
Variable Coefficient Std. Error t-Statistic Prob. C 0.005896 0.000191 30.85979 0.0000 AR(4) 0.423205 0.144961 2.919443 0.0051 MA(4) -0.916586 0.045960 -19.94314 0.0000 R-squared 0.206277 Mean dependent var 0.006104 Adjusted R-squared 0.176879 S.D. dependent var 0.003599 S.E. of regression 0.003265 Akaike info criterion -8.559816 Sum squared resid 0.000576 Schwarz criterion -8.452287 Log likelihood 246.9547 F-statistic 7.016884
Inverted AR Roots .81 .00 -.81i .00+.81i -.81 Inverted MA Roots .98
Bảng 3
ADF Test Statistic -8.662621 1% Critical Value* -2.6040 5% Critical Value -1.9464 10% Critical Value -1.6188 *MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(E2)
Method: Least Squares Date: 06/07/07 Time: 14:53 Sample(adjusted): 6 61
Included observations: 56 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob. E1(-1) -1.137463 0.131307 -8.662621 0.0000 R-squared 0.577015 Mean dependent var -4.74E-05 Adjusted R-squared 0.577015 S.D. dependent var 0.004824 S.E. of regression 0.003137 Akaike info criterion -8.673198 Sum squared resid 0.000541 Schwarz criterion -8.637031 Log likelihood 243.8495 Durbin-Watson stat 2.062360
Đồ thị lược đồ tương quan của chuỗi số liệu e1
Date: 06/07/07 Time: 14:55 Sample: 1 61
Included observations: 57
Autocorrelation Partial Correlation AC PAC Q-Stat Prob .*| . | .*| . | 1 -0.138 -0.138 1.1362 0.286 .*| . | .*| . | 2 -0.074 -0.094 1.4668 0.480 . | . | . | . | 3 0.058 0.035 1.6765 0.642 . | . | . | . | 4 0.008 0.015 1.6805 0.794 . |*. | . |*. | 5 0.092 0.106 2.2226 0.818 . | . | . | . | 6 0.010 0.040 2.2292 0.897 . |*. | . |*. | 7 0.069 0.094 2.5456 0.924 . |*. | . |*. | 8 0.104 0.128 3.2867 0.915 .*| . | .*| . | 9 -0.157 -0.121 5.0118 0.833 . |*. | . |*. | 10 0.105 0.067 5.7974 0.832 . | . | . | . | 11 -0.006 -0.028 5.8002 0.886 .*| . | .*| . | 12 -0.165 -0.180 7.8410 0.797
. |*. | . |*. | 13 0.165 0.097 9.9217 0.700 .*| . | .*| . | 14 -0.082 -0.076 10.449 0.729 .*| . | .*| . | 14 -0.082 -0.076 10.449 0.729 . |*. | . |*. | 15 0.153 0.165 12.314 0.655 . | . | . | . | 16 -0.019 0.023 12.345 0.720 .*| . | . | . | 17 -0.100 -0.035 13.183 0.724 .*| . | **| . | 18 -0.121 -0.210 14.438 0.700 .*| . | .*| . | 19 -0.061 -0.095 14.769 0.737 . | . | .*| . | 20 -0.006 -0.092 14.772 0.789 . | . | .*| . | 21 -0.035 -0.131 14.886 0.829 .*| . | . | . | 22 -0.075 -0.019 15.421 0.844 . | . | . | . | 23 0.012 -0.044 15.435 0.878 .*| . | . | . | 24 -0.104 -0.034 16.528 0.868 Bảng 4 Dependent Variable: TL
Method: ML - ARCH (Marquardt) Date: 06/07/07 Time: 15:00 Sample(adjusted): 5 61
Included observations: 57 after adjusting endpoints Convergence achieved after 25 iterations
MA backcast: 1 4, Variance backcast: ON
Coefficient Std. Error z-Statistic Prob. C 0.005898 0.000198 29.74113 0.0000 AR(4) 0.459472 0.180894 2.540003 0.0111 MA(4) -0.915974 0.049192 -18.62021 0.0000 Variance Equation C 1.13E-05 4.03E-06 2.800624 0.0051 ARCH(1) -0.116542 0.223838 -0.520655 0.6026 R-squared 0.205076 Mean dependent var 0.006104 Adjusted R-squared 0.143928 S.D. dependent var 0.003599 S.E. of regression 0.003330 Akaike info criterion -8.498693 Sum squared resid 0.000577 Schwarz criterion -8.319478 Log likelihood 247.2127 F-statistic 3.353768 Durbin-Watson stat 2.232802 Prob(F-statistic) 0.016218 Inverted AR Roots .82 .00 -.82i
Inverted MA Roots .98 .00+.98i -.00 -.98i -.98
Method: ML - ARCH (Marquardt) Date: 06/07/07 Time: 15:03 Sample(adjusted): 5 61
Included observations: 57 after adjusting endpoints Convergence achieved after 27 iterations
MA backcast: 1 4, Variance backcast: ON
Coefficient Std. Error z-Statistic Prob. C 0.005911 0.000208 28.46841 0.0000 AR(4) 0.465948 0.178864 2.605046 0.0092 MA(4) -0.915219 0.050219 -18.22466 0.0000 Variance Equation C 8.28E-06 2.07E-05 0.400436 0.6888 ARCH(1) -0.119454 0.222411 -0.537088 0.5912 GARCH(1) 0.292531 2.020924 0.144751 0.8849 R-squared 0.204446 Mean dependent var 0.006104 Adjusted R-squared 0.126450 S.D. dependent var 0.003599 S.E. of regression 0.003364 Akaike info criterion -8.465286 Sum squared resid 0.000577 Schwarz criterion -8.250228 Log likelihood 247.2607 F-statistic 2.621254 Durbin-Watson stat 2.234183 Prob(F-statistic) 0.034825 Inverted AR Roots .83 .00 -.83i .00+.83i -.83 Inverted MA Roots .98 -.00+.98i -.00 -.98i -.98
Bảng 6
Dependent Variable: TL
Method: ML - ARCH (Marquardt) Date: 06/07/07 Time: 16:12 Sample(adjusted): 5 61
Included observations: 57 after adjusting endpoints Convergence achieved after 62 iterations
MA backcast: 1 4, Variance backcast: ON
Coefficient Std. Error z-Statistic Prob. SQR(GARCH) -3.971692 0.661447 -6.004549 0.0000 C 0.031864 0.001543 20.64626 0.0000 AR(4) 0.137628 0.040557 3.393412 0.0007 MA(4) -0.136210 0.201244 -0.676838 0.4985 Variance Equation C -1.51E-05 9.06E-10 -16712.32 0.0000 ARCH(1) 0.221312 0.036000 6.147618 0.0000 GARCH(1) 1.275156 0.048601 26.23743 0.0000
R-squared -0.704581 Mean dependent var 0.006104 Adjusted R-squared -0.909131 S.D. dependent var 0.003599 S.E. of regression 0.004973 Akaike info criterion -6.081768 Sum squared resid 0.001236 Schwarz criterion -5.830867 Log likelihood 180.3304 Durbin-Watson stat 1.916742 Inverted AR Roots .61 .00 -.61i
Inverted MA Roots .61 .00 -.61i
Bảng 7
Dependent Variable: TL
Method: ML - ARCH (Marquardt) Date: 06/07/07 Time: 15:11 Sample(adjusted): 5 61
Included observations: 57 after adjusting endpoints Convergence achieved after 34 iterations
MA backcast: 1 4, Variance backcast: ON
Coefficient Std. Error z-Statistic Prob. C 0.005887 0.000201 29.28968 0.0000 AR(4) 0.427291 0.173644 2.460730 0.0139 MA(4) -0.928953 0.036608 -25.37564 0.0000 Variance Equation C 1.07E-05 1.40E-05 0.763074 0.4454 ARCH(1) 0.004341 0.432447 0.010039 0.9920 (RESID<0)*ARCH(1) -0.251631 0.392175 -0.641628 0.5211 GARCH(1) 0.066396 1.399256 0.047451 0.9622 R-squared 0.204262 Mean dependent var 0.006104 Adjusted R-squared 0.108774 S.D. dependent var 0.003599 S.E. of regression 0.003398 Akaike info criterion -8.456349 Sum squared resid 0.000577 Schwarz criterion -8.205448 Log likelihood 248.0059 F-statistic 2.139128 Durbin-Watson stat 2.234976 Prob(F-statistic) 0.065010 Inverted AR Roots .81 .00 -.81i .00+.81i -.81 Inverted MA Roots .98 .00+.98i -.00 -.98i -.98
Method: ML - ARCH (Marquardt) Date: 06/07/07 Time: 15:14 Sample(adjusted): 5 61
Included observations: 57 after adjusting endpoints Convergence achieved after 37 iterations
MA backcast: 1 4, Variance backcast: ON
Coefficient Std. Error z-Statistic Prob. C 0.005854 0.000209 28.04813 0.0000 AR(4) 0.457552 0.168701 2.712213 0.0067 MA(4) -0.926496 0.040187 -23.05438 0.0000 Variance Equation C -10.48001 13.38091 -0.783206 0.4335 |RES|/SQR[GARCH](1) -0.337775 0.758360 -0.445402 0.6560 RES/SQR[GARCH](1) 0.165273 0.307329 0.537773 0.5907 EGARCH(1) 0.065804 1.184248 0.055566 0.9557 R-squared 0.204049 Mean dependent var 0.006104 Adjusted R-squared 0.108534 S.D. dependent var 0.003599 S.E. of regression 0.003398 Akaike info criterion -8.444932 Sum squared resid 0.000577 Schwarz criterion -8.194031 Log likelihood 247.6806 F-statistic 2.136318 Durbin-Watson stat 2.237024 Prob(F-statistic) 0.065335 Inverted AR Roots .82 .00 -.82i
Inverted MA Roots .98 .00+.98i -.00 -.98i -.98
0.E+00 2.E+12 4.E+12 6.E+12 8.E+12 1.E+13 10 20 30 40 50 60 DUNO Đồ thị dự báo tỷ lệ nợ quá hạn -.004 .000 .004 .008 .012 .016 5 10 15 20 25 30 35 40 45 50 55 60 TLF Forecast: TLF Actual: TL Forecast sample: 1 61 Adjusted sample: 5 61 Included observations: 57
Root Mean Squared Error 0.003599 Mean Absolute Error 0.003172 Mean Abs. Percent Error 194.0529 Theil Inequality Coefficient 0.273570 Bias Proportion 0.000204 Variance Proportion 0.671458 Covariance Proportion 0.328339
Đồ thị chuỗi KNMV .0000 .0004 .0008 .0012 .0016 .0020 10 20 30 40 50 60 KNMV
Sử dụng phần mền Eviews trong kinh tế lượng ta ước lượng các mô hình cho ra các bảng kết quả như sau:
Bảng 9
ADF Test Statistic -7.984708 1% Critical Value* -4.1162 5% Critical Value -3.4849 10% Critical Value -3.1703 *MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(KNMV)
Method: Least Squares Date: 06/08/07 Time: 23:15 Sample(adjusted): 2 61
Included observations: 60 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob. KNMV(-1) -0.951829 0.119207 -7.984708 0.0000 C 0.000940 0.000142 6.595882 0.0000 @TREND(1) -1.34E-05 2.62E-06 -5.132539 0.0000 R-squared 0.530520 Mean dependent var -2.99E-05 Adjusted R-squared 0.514047 S.D. dependent var 0.000353 S.E. of regression 0.000246 Akaike info criterion -13.73250 Sum squared resid 3.45E-06 Schwarz criterion -13.62778 Log likelihood 414.9750 F-statistic 32.20545 Durbin-Watson stat 2.160164 Prob(F-statistic) 0.000000
Bảng 10
Dependent Variable: KNMV Method: Least Squares Date: 06/08/07 Time: 23:20 Sample(adjusted): 2 61
Included observations: 60 after adjusting endpoints Convergence achieved after 11 iterations
Backcast: 1
Variable Coefficient Std. Error t-Statistic Prob. AR(1) 0.973897 0.003269 297.8831 0.0000 MA(1) -0.983527 0.011344 -86.70301 0.0000 R-squared 0.524007 Mean dependent var 0.000558 Adjusted R-squared 0.515800 S.D. dependent var 0.000347 S.E. of regression 0.000241 Akaike info criterion -13.78840 Sum squared resid 3.38E-06 Schwarz criterion -13.71859 Log likelihood 415.6521 Durbin-Watson stat 2.087106
Inverted MA Roots .98
Bảng 11
ADF Test Statistic -8.207608 1% Critical Value* -2.6019 5% Critical Value -1.9460 10% Critical Value -1.6187 *MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(E1)
Method: Least Squares Date: 06/08/07 Time: 23:22 Sample(adjusted): 3 61
Included observations: 59 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob. E2(-1) -1.060708 0.129235 -8.207608 0.0000 R-squared 0.537148 Mean dependent var -7.22E-06 Adjusted R-squared 0.537148 S.D. dependent var 0.000349 S.E. of regression 0.000237 Akaike info criterion -13.83937 Sum squared resid 3.26E-06 Schwarz criterion -13.80416 Log likelihood 409.2615 Durbin-Watson stat 2.019603
Đồ thị lược đồ tương quan của chuỗi số liệu e2
Date: 06/09/07 Time: 16:23 Sample: 1 61
Included observations: 60
Autocorrelation Partial Correlation AC PAC Q-Stat Prob .*| . | .*| . | 1 -0.063 -0.063 0.2484 0.618 .*| . | .*| . | 2 -0.088 -0.093 0.7505 0.687 . | . | . | . | 3 0.046 0.034 0.8875 0.828 .*| . | .*| . | 4 -0.140 -0.145 2.1846 0.702 . |*. | . |*. | 5 0.188 0.183 4.5625 0.472 . | . | . | . | 6 -0.014 -0.027 4.5764 0.599 . | . | . |*. | 7 0.044 0.098 4.7106 0.695 . |*. | . |*. | 8 0.097 0.066 5.3817 0.716 .*| . | . | . | 9 -0.059 0.016 5.6397 0.775 .*| . | .*| . | 10 -0.087 -0.127 6.2072 0.798 .*| . | .*| . | 11 -0.090 -0.094 6.8247 0.813
. | . | . | . | 12 -0.012 -0.053 6.8362 0.868 .*| . | .*| . | 13 -0.080 -0.142 7.3447 0.884 .*| . | .*| . | 13 -0.080 -0.142 7.3447 0.884 . | . | . | . | 14 -0.016 -0.049 7.3650 0.920 .*| . | **| . | 15 -0.156 -0.203 9.3722 0.857 . | . | . | . | 16 0.007 0.018 9.3767 0.897 . |** | . |*. | 17 0.205 0.192 13.008 0.736 .*| . | . |*. | 18 -0.058 0.069 13.310 0.773 .*| . | .*| . | 19 -0.088 -0.063 14.006 0.783 .*| . | . | . | 20 -0.088 -0.050 14.729 0.792 .*| . | .*| . | 21 -0.123 -0.135 16.171 0.760 . |*. | . | . | 22 0.078 -0.033 16.761 0.776 . | . | .*| . | 23 -0.033 -0.099 16.869 0.816 . | . | .*| . | 24 0.007 -0.069 16.874 0.854 . | . | .*| . | 25 0.013 -0.110 16.892 0.886 .*| . | . | . | 26 -0.068 -0.043 17.405 0.896 . | . | . | . | 27 -0.010 0.014 17.416 0.920 . | . | . |*. | 28 0.000 0.066 17.416 0.940 Bảng 12 Dependent Variable: KNMV Method: ML - ARCH (Marquardt) Date: 06/08/07 Time: 23:52 Sample(adjusted): 2 61
Included observations: 60 after adjusting endpoints Convergence achieved after 79 iterations
MA backcast: 1, Variance backcast: ON
Coefficient Std. Error z-Statistic Prob. AR(1) 0.974483 0.004501 216.5150 0.0000 MA(1) -0.982370 0.016911 -58.09100 0.0000
Variance Equation
C 5.78E-08 6.21E-09 9.304737 0.0000ARCH(1) -0.037883 0.113518 -0.333714 0.7386 ARCH(1) -0.037883 0.113518 -0.333714 0.7386 R-squared 0.523722 Mean dependent var 0.000558 Adjusted R-squared 0.498207 S.D. dependent var 0.000347 S.E. of regression 0.000246 Akaike info criterion -13.74260 Sum squared resid 3.38E-06 Schwarz criterion -13.60298 Log likelihood 416.2781 Durbin-Watson stat 2.089699 Inverted AR Roots .97
Inverted MA Roots .98
Dependent Variable: KNMV Method: ML - ARCH (Marquardt) Date: 06/09/07 Time: 00:08 Sample(adjusted): 2 61
Included observations: 60 after adjusting endpoints Convergence achieved after 22 iterations
MA backcast: 1, Variance backcast: ON
Coefficient Std. Error z-Statistic Prob. AR(1) 0.915207 0.026349 34.73365 0.0000 MA(1) -0.488830 0.105126 -4.649931 0.0000 Variance Equation C -2.67E-10 1.16E-09 -0.229588 0.8184 ARCH(1) -0.042499 0.008398 -5.060829 0.0000 GARCH(1) 1.064739 0.027468 38.76351 0.0000 R-squared 0.336214 Mean dependent var 0.000558 Adjusted R-squared 0.287939 S.D. dependent var 0.000347 S.E. of regression 0.000293 Akaike info criterion -13.64136 Sum squared resid 4.71E-06 Schwarz criterion -13.46683 Log likelihood 414.2408 Durbin-Watson stat 2.329826 Inverted AR Roots .92
Inverted MA Roots .49
Bảng 14
Dependent Variable: KNMV Method: ML - ARCH (Marquardt) Date: 06/09/07 Time: 00:32 Sample(adjusted): 2 61
Included observations: 60 after adjusting endpoints Convergence achieved after 21 iterations
MA backcast: 1, Variance backcast: ON
Coefficient Std. Error z-Statistic Prob. SQR(GARCH) 2.034640 0.397998 5.112188 0.0000 AR(1) 0.260175 0.273166 0.952443 0.3409 MA(1) -0.011645 0.375031 -0.031051 0.9752 Variance Equation C -4.50E-10 1.01E-09 -0.447834 0.6543 ARCH(1) -0.035549 0.012027 -2.955778 0.0031 GARCH(1) 1.017429 0.016793 60.58569 0.0000 R-squared 0.453206 Mean dependent var 0.000558 Adjusted R-squared 0.402577 S.D. dependent var 0.000347 S.E. of regression 0.000268 Akaike info criterion -13.75214 Sum squared resid 3.88E-06 Schwarz criterion -13.54271
Log likelihood 418.5643 Durbin-Watson stat 2.172054 Inverted AR Roots .26
Inverted MA Roots .01
Bảng 15
Dependent Variable: KNMV Method: ML - ARCH (Marquardt) Date: 06/09/07 Time: 00:55 Sample(adjusted): 2 61
Included observations: 60 after adjusting endpoints Convergence achieved after 9 iterations
MA backcast: 1, Variance backcast: ON
Coefficient Std. Error z-Statistic Prob. AR(1) 0.967194 0.067966 14.23054 0.0000 MA(1) -0.167017 0.206111 -0.810325 0.4178 Variance Equation C 5.02E-08 1.00E-07 0.499934 0.6171 ARCH(1) -0.048989 0.042041 -1.165265 0.2439 (RESID<0)*ARCH(1) -0.069354 0.374487 -0.185198 0.8531 GARCH(1) 0.668793 0.714649 0.935833 0.3494 R-squared 0.133568 Mean dependent var 0.000558 Adjusted R-squared 0.053343 S.D. dependent var 0.000347 S.E. of regression 0.000337 Akaike info criterion -12.91911 Sum squared resid 6.15E-06 Schwarz criterion -12.70968 Log likelihood 393.5734 Durbin-Watson stat 2.698514 Inverted AR Roots .97
Inverted MA Roots .17
Bảng 16
Dependent Variable: KNMV Method: ML - ARCH (Marquardt) Date: 06/09/07 Time: 01:11 Sample(adjusted): 2 61
Included observations: 60 after adjusting endpoints Convergence achieved after 37 iterations
MA backcast: 1, Variance backcast: ON
Coefficient Std. Error z-Statistic Prob. AR(1) 0.942077 0.014467 65.11866 0.0000 MA(1) -0.730517 0.038876 -18.79073 0.0000
|RES|/SQR[GARCH](1) -0.948617 0.367346 -2.582350 0.0098RES/SQR[GARCH](1) -0.525563 0.334060 -1.573257 0.1157 RES/SQR[GARCH](1) -0.525563 0.334060 -1.573257 0.1157 EGARCH(1) -0.036696 0.403541 -0.090935 0.9275 R-squared 0.417468 Mean dependent var 0.000558 Adjusted R-squared 0.363530 S.D. dependent var 0.000347 S.E. of regression 0.000277 Akaike info criterion -13.74493 Sum squared resid 4.13E-06 Schwarz criterion -13.53549 Log likelihood 418.3478 Durbin-Watson stat 2.124014 Inverted AR Roots .94 Inverted MA Roots .73 Đồ thị dự báo khả năng mầt vốn -.0005 .0000 .0005 .0010 .0015 .0020 .0025 5 10 15 20 25 30 35 40 45 50 55 60 KNMVF Forecast: KNMVF Actual: KNMV Forecast sample: 1 61 Adjusted sample: 2 61 Included observations: 60
Root Mean Squared Error 0.000490 Mean Absolute Error 0.000434 Mean Abs. Percent Error 99.55947 Theil Inequality Coefficient 0.289112 Bias Proportion 0.632978 Variance Proportion 0.027726 Covariance Proportion 0.339295