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Построение эконометрической модели и исследование проблемы автокорреляции с помощью тестов Бреуша

Построение эконометрической модели и исследование проблемы автокорреляции с помощью тестов Бреуша


1.1 Экономическое обоснование модели


ADF Test Statistic -20.99004 1% Critical Value* -4.2412
5% Critical Value -3.5426
10% Critical Value -3.2032
Dependent Variable: D(IG)
Method: Least Squares
Included observations: 35 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(IG(-1)) -2.200495 0.104835 -20.99004 0.0000
@TREND(1999:1) 9.663892 2.439289 3.961766 0.0004
Durbin-Watson stat 2.352758 Prob(F-statistic) 0.000000
ADF Test Statistic -5.278444 1% Critical Value* -4.2412
5% Critical Value -3.5426
10% Critical Value -3.2032
Dependent Variable: D(CONS)
Method: Least Squares
Included observations: 35 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(CONS(-1)) -1.636006 0.309941 -5.278444 0.0000
@TREND(1999:1) 12.54844 3.021702 4.152773 0.0002
Durbin-Watson stat 2.101394 Prob(F-statistic) 0.000000
ADF Test Statistic -9.618956 1% Critical Value* -4.2412
5% Critical Value -3.5426
10% Critical Value -3.2032
Dependent Variable: D(GDP)
Method: Least Squares
Included observations: 35 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(GDP(-1)) -2.088636 0.217137 -9.618956 0.0000
@TREND(1999:1) 26.31412 6.414595 4.102226 0.0003
Durbin-Watson stat 2.486933 Prob(F-statistic) 0.000000
Dependent Variable: GDP
Method: Least Squares
Date: 12/11/08 Time: 16:34
Sample: 1999:1 2008:2
Included observations: 38
GDP=C(1)+C(2)*Cons+C(3)*IG
Coefficient Std. Error t-Statistic Prob.
C(1) 90.71828 36.69767 2.472045 0.0184
C(2) 0.875856 0.076378 11.46745 0.0000
C(3) 1.190895 0.030510 39.03232 0.0000
R-squared 0.998324 Mean dependent var 4283.858
Adjusted R-squared 0.998228 S.D. dependent var 2609.517
S.E. of regression 109.8386 Akaike info criterion 12.31156
Sum squared resid 422257.9 Schwarz criterion 12.44084
Log likelihood -230.9196 Durbin-Watson stat 0.589082
White Heteroskedasticity Test:
F-statistic 1.926499 Probability 0.129239
Obs*R-squared 7.193728 Probability 0.125998
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 12/11/08 Time: 19:18
Sample: 1999:1 2008:2
Included observations: 38
Variable Coefficient Std. Error t-Statistic Prob.
C -7329.568 8035.888 -0.912104 0.3683
IG -10.79329 22.84694 -0.472417 0.6397
IG^2 0.000343 0.007396 0.046398 0.9633
CONS 14.94592 10.01542 1.492291 0.1451
CONS^2 -0.001335 0.001299 -1.028002 0.3114
R-squared 0.189309 Mean dependent var 11112.05
Adjusted R-squared 0.091043 S.D. dependent var 13500.26
S.E. of regression 12871.05 Akaike info criterion 21.88543
Sum squared resid 5.47E+09 Schwarz criterion 22.10090
Log likelihood -410.8231 F-statistic 1.926499
Durbin-Watson stat 1.289207 Prob(F-statistic) 0.129239
White Heteroskedasticity Test:
F-statistic 1.910945 Probability 0.120009
Obs*R-squared 8.737384 Probability 0.120009
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 12/11/08 Time: 19:20
Sample: 1999:1 2008:2
Included observations: 38
Variable Coefficient Std. Error t-Statistic Prob.
C -4788.651 8190.315 -0.584672 0.5629
IG 10.01788 27.71085 0.361515 0.7201
IG^2 0.043812 0.034248 1.279250 0.2100
IG*CONS -0.034393 0.026471 -1.299253 0.2031
CONS 5.948824 12.09186 0.491969 0.6261
CONS^2 0.005437 0.005368 1.012743 0.3188
R-squared 0.229931 Mean dependent var 11112.05
Adjusted R-squared 0.109608 S.D. dependent var 13500.26
S.E. of regression 12738.93 Akaike info criterion 21.88665
Sum squared resid 5.19E+09 Schwarz criterion 22.14522
Log likelihood -409.8464 F-statistic 1.910945
Durbin-Watson stat 1.168906 Prob(F-statistic) 0.120009

Глава 3. Устранение автокорреляции

Breusch-Godfrey Serial Correlation LM Test:
F-statistic 33.14949 Probability 0.000002
Obs*R-squared 18.75935 Probability 0.000015
Test Equation:
Dependent Variable: RESID
Method: Least Squares
Date: 12/11/08 Time: 19:17
Presample missing value lagged residuals set to zero.
Variable Coefficient Std. Error t-Statistic Prob.
C(1) 4.195415 26.50424 0.158292 0.8752
C(2) 0.046689 0.055735 0.837705 0.4080
C(3) -0.016381 0.022210 -0.737543 0.4659
RESID(-1) 0.710963 0.123483 5.757559 0.0000
R-squared 0.493667 Mean dependent var -6.15E-13
Adjusted R-squared 0.448991 S.D. dependent var 106.8287
S.E. of regression 79.29897 Akaike info criterion 11.68363
Sum squared resid 213803.1 Schwarz criterion 11.85601
Log likelihood -217.9889 Durbin-Watson stat 1.935910
Dependent Variable: GDP
Method: Least Squares
Date: 12/11/08 Time: 19:23
Sample: 1999:1 2008:2
Included observations: 38
GDP=C(1)+C(2)*IG+C(3)*CONS+C(4)*NX
Coefficient Std. Error t-Statistic Prob.
C(1) 9.983102 15.40599 0.648001 0.5213
C(2) 1.041238 0.031994 32.54493 0.0000
C(3) 1.004281 0.017836 36.30674 0.0000
C(4) 0.890623 0.063486 14.02859 0.0000
R-squared 0.999753 Mean dependent var 4283.858
Adjusted R-squared 0.999731 S.D. dependent var 2609.517
S.E. of regression 42.77300 Akaike info criterion 10.44899
Sum squared resid 62204.00 Schwarz criterion 10.62137
Log likelihood -194.5308 Durbin-Watson stat 2.338553
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 1.250798 Probability 0.271476
Obs*R-squared 1.387714 Probability 0.238791
Test Equation:
Dependent Variable: RESID
Method: Least Squares
Date: 12/11/08 Time: 19:25
Presample missing value lagged residuals set to zero.
Variable Coefficient Std. Error t-Statistic Prob.
C(1) -2.488241 15.50988 -0.160429 0.8735
C(2) -0.011896 0.033604 -0.353999 0.7256
C(3) 0.003454 0.018037 0.191509 0.8493
C(4) 0.007246 0.063584 0.113957 0.9100
RESID(-1) -0.208047 0.186023 -1.118391 0.2715
R-squared 0.036519 Mean dependent var -1.42E-12
Adjusted R-squared -0.080267 S.D. dependent var 41.00231
S.E. of regression 42.61611 Akaike info criterion 10.46442
Sum squared resid 59932.38 Schwarz criterion 10.67989
Log likelihood -193.8240 Durbin-Watson stat 1.998121



AC PAC Q-Stat Prob
1 -0.162 -0.162 1.0715 0.301
2 -0.156 -0.187 2.0992 0.350
3 0.064 0.004 2.2754 0.517
4 0.387 0.394 8.9637 0.062
5 -0.352 -0.245 14.681 0.012
6 -0.146 -0.178 15.697 0.015
7 0.157 0.015 16.901 0.018
8 0.091 -0.011 17.317 0.027
9 -0.101 -0.099 29.374 0.001
10 0.107 0.041 29.997 0.001
11 0.083 -0.117 30.385 0.001
12 -0.066 -0.062 30.637 0.002
13 -0.163 0.132 32.256 0.002
14 0.104 -0.202 32.947 0.003
15 0.073 -0.022 33.303 0.004
16 -0.142 -0.057 34.694 0.004

Приложение 3

ADF Test Statistic -5.278444 1% Critical Value* -4.2412
5% Critical Value -3.5426
10% Critical Value -3.2032
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(CONS)
Method: Least Squares
Date: 12/11/08 Time: 19:00
Sample(adjusted): 1999:4 2008:2
Included observations: 35 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(CONS(-1)) -1.636006 0.309941 -5.278444 0.0000
@TREND(1999:1) 12.54844 3.021702 4.152773 0.0002
R-squared 0.719844 Mean dependent var 11.88857
Adjusted R-squared 0.692732 S.D. dependent var 211.7761
S.E. of regression 117.3913 Akaike info criterion 12.47611
Sum squared resid 427201.9 Schwarz criterion 12.65387
Log likelihood -214.3320 F-statistic 26.55085
Durbin-Watson stat 2.101394 Prob(F-statistic) 0.000000
ADF Test Statistic -20.99004 1% Critical Value* -4.2412
5% Critical Value -3.5426
10% Critical Value -3.2032
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(IG)
Method: Least Squares
Date: 12/11/08 Time: 18:56
Sample(adjusted): 1999:4 2008:2
Included observations: 35 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(IG(-1)) -2.200495 0.104835 -20.99004 0.0000
@TREND(1999:1) 9.663892 2.439289 3.961766 0.0004
R-squared 0.935547 Mean dependent var 19.71143
Adjusted R-squared 0.929310 S.D. dependent var 541.9242
S.E. of regression 144.0849 Akaike info criterion 12.88589
Sum squared resid 643574.0 Schwarz criterion 13.06365
Log likelihood -221.5031 F-statistic 149.9904
Durbin-Watson stat 2.352758 Prob(F-statistic) 0.000000
ADF Test Statistic -9.618956 1% Critical Value* -4.2412
5% Critical Value -3.5426
10% Critical Value -3.2032
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(GDP)
Method: Least Squares
Date: 12/11/08 Time: 19:12
Sample(adjusted): 1999:4 2008:2
Included observations: 35 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(GDP(-1)) -2.088636 0.217137 -9.618956 0.0000
@TREND(1999:1) 26.31412 6.414595 4.102226 0.0003
R-squared 0.775601 Mean dependent var 33.28571
Adjusted R-squared 0.753884 S.D. dependent var 717.4181
S.E. of regression 355.9113 Akaike info criterion 14.69445
Sum squared resid 3926860. Schwarz criterion 14.87221
Log likelihood -253.1529 F-statistic 35.71550
Durbin-Watson stat 2.486933 Prob(F-statistic) 0.000000
PP Test Statistic -6.168609 1% Critical Value* -4.2324
5% Critical Value -3.5386
10% Critical Value -3.2009
*MacKinnon critical values for rejection of hypothesis of a unit root.
Lag truncation for Bartlett kernel: 1 ( Newey-West suggests: 3 )
Residual variance with no correction 128108.6
Residual variance with correction 114483.1
Phillips-Perron Test Equation
Dependent Variable: D(IG)
Method: Least Squares
Date: 12/13/08 Time: 14:39
Sample(adjusted): 1999:3 2008:2
Included observations: 36 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(IG(-1)) -1.133453 0.183759 -6.168167 0.0000
@TREND(1999:1) 3.839129 5.997744 2.640095 0.1265
R-squared 0.438149 Mean dependent var 20.35833
Adjusted R-squared 0.510158 S.D. dependent var 534.1404
S.E. of regression 373.8380 Akaike info criterion 14.76518
Sum squared resid 4611909. Schwarz criterion 14.89714
Log likelihood -262.7732 F-statistic 19.22581
Durbin-Watson stat 2.134551 Prob(F-statistic) 0.000003
PP Test Statistic -10.63290 1% Critical Value* -4.2324
5% Critical Value -3.5386
10% Critical Value -3.2009
*MacKinnon critical values for rejection of hypothesis of a unit root.
Lag truncation for Bartlett kernel: 3 ( Newey-West suggests: 3 )
Residual variance with no correction 200449.2
Residual variance with correction 30674.85
Phillips-Perron Test Equation
Dependent Variable: D(GDP)
Method: Least Squares
Date: 12/13/08 Time: 14:44
Sample(adjusted): 1999:3 2008:2
Included observations: 36 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(GDP(-1)) -1.243348 0.182298 -6.820400 0.0000
@TREND(1999:1) 14.23606 7.613909 2.869744 0.0704
R-squared 0.587667 Mean dependent var 34.34444
Adjusted R-squared 0.562677 S.D. dependent var 707.1235
S.E. of regression 467.6236 Akaike info criterion 15.21286
Sum squared resid 7216171. Schwarz criterion 15.34482
Log likelihood -270.8315 F-statistic 23.51620
Durbin-Watson stat 2.209326 Prob(F-statistic) 0.000000
OBS Nx Cons IG GDP
1999:1 123.9 708 69.4 901.3
1999:2 165.1 766.3 170.1 1101.5
1999:3 206.8 852.5 313.8 1373.1
1999:4 326.4 958.9 162 1447.3
2000:1 372.3 997.7 177 1527.4
2000:2 388.6 1045.1 283.2 1696.6
2000:3 372.2 1167.3 470.1 2037.8
2000:4 330 1266.7 435.4 2043.8
2001:1 357.1 1306.3 253.7 1900.9
2001:2 294.7 1412.7 409.6 2105
2001:3 274.5 1523.9 682.7 2487.9
2001:4 207.4 1643.9 617.1 2449.8
2002:1 235.7 1691 333.5 2259.5
2002:2 290.7 1779.9 456.4 2525.7
2002:3 329.7 1907 745.5 3009.2
2002:4 311.4 2070.9 635.1 3023.1
2003:1 414 2071.1 382.5 2850.7
2003:2 351.5 2165.8 580.3 3107.8
2003:3 360.2 2289.9 985.2 3629.8
2003:4 376.3 2497.9 807.1 3655
2004:1 425.5 2584.7 493 3516.8
2004:2 495 2714.9 760.3 3969.8
2004:3 557.5 2919.6 1206.5 4615.2
2004:4 608.5 3182.3 1099.1 4946.4
2005:1 617.1 3170.8 677.7 4459.7
2005:2 763.1 3460.5 876.4 5080.4
2005:3 788.8 3686.6 1470.5 5873
2005:4 790 4001 1314.1 6212.3
2006:1 961.6 3960.9 899.5 5845.3
2006:2 944.4 4239.8 1223.4 6361.3
2006:3 877.9 4520.5 1860.5 7280.6
2006:4 638.6 4894.8 1753.4 7392.5
2007:1 679.3 4818.8 1263.8 6747.9
2007:2 687.8 5231.2 1764.1 7749.1
2007:3 641.8 5599.9 2530 8826.6
2007:4 861.6 6161 2544.1 9663.7