Model 1: OLS, using observations 1980-2017 (T = 38)
Dependent variable: GDP
coefficient std. error t-ratio p-value
---------------------------------------------------------
const −288976 17853.5 −16.19 4.22e-018 ***
CPI 17058.6 262.372 65.02 6.32e-039 ***
Mean dependent var 787903.9 S.D. dependent var 440968.1
Sum squared resid 6.08e+10 S.E. of regression 41080.96
R-squared 0.991556 Adjusted R-squared 0.991321
F(1, 36) 4227.193 P-value(F) 6.32e-39
Log-likelihood −456.5778 Akaike criterion 917.1556
Schwarz criterion 920.4307 Hannan-Quinn 918.3209
rho 0.684402 Durbin-Watson 0.586765
오차항의 AR(1)에 대한 테스트
LM test for autocorrelation up to order 1 -
Null hypothesis: no autocorrelation
Test statistic: LMF = 24.5724
with p-value = P(F(1, 35) > 24.5724) = 1.82637e-005
Breusch-Godfrey test for first-order autocorrelation
OLS, using observations 1980-2017 (T = 38)
Dependent variable: uhat
coefficient std. error t-ratio p-value
-----------------------------------------------------------
const −4450.01 13907.8 −0.3200 0.7509
CPI 96.2531 204.883 0.4698 0.6414
uhat_1 0.693349 0.139871 4.957 1.83e-05 ***
Unadjusted R-squared = 0.412479
Alternative statistic: TR^2 = 15.674219,
with p-value = P(Chi-square(1) > 15.6742) = 7.52e-005
GDP에 대한 correlogram ACF, PACF
Autocorrelation function for GDP
***, **, * indicate significance at the 1%, 5%, 10% levels
using standard error 1/T^0.5
LAG ACF PACF Q-stat. [p-value]
1 0.9271 *** 0.9271 *** 35.3131 [0.000]
2 0.8532 *** -0.0457 66.0477 [0.000]
3 0.7783 *** -0.0464 92.3547 [0.000]
4 0.7027 *** -0.0475 114.4274 [0.000]
5 0.6271 *** -0.0439 132.5397 [0.000]
6 0.5501 *** -0.0561 146.9160 [0.000]
7 0.4721 *** -0.0573 157.8456 [0.000]
8 0.3958 ** -0.0406 165.7834 [0.000]
9 0.3250 ** -0.0147 171.3197 [0.000]
10 0.2515 -0.0733 174.7544 [0.000]
11 0.1790 -0.0518 176.5592 [0.000]
12 0.1106 -0.0319 177.2747 [0.000]
13 0.0455 -0.0380 177.4008 [0.000]
14 -0.0173 -0.0483 177.4198 [0.000]
15 -0.0758 -0.0335 177.7996 [0.000]
16 -0.1311 -0.0420 178.9876 [0.000]
17 -0.1797 -0.0176 181.3257 [0.000]
18 -0.2249 -0.0424 185.1681 [0.000]
19 -0.2697 * -0.0644 190.9892 [0.000]
20 -0.3030 * 0.0171 198.7406 [0.000]
21 -0.3379 ** -0.0767 208.9504 [0.000]
22 -0.3683 ** -0.0363 221.8396 [0.000]
23 -0.3909 ** -0.0091 237.3210 [0.000]
24 -0.4077 ** -0.0212 255.3684 [0.000]
25 -0.4175 ** -0.0091 275.7534 [0.000]
26 -0.4223 *** -0.0215 298.3421 [0.000]
27 -0.4211 *** -0.0103 322.8435 [0.000]
28 -0.4116 ** 0.0159 348.5968 [0.000]
29 -0.3966 ** -0.0078 375.1646 [0.000]
30 -0.3794 ** -0.0214 402.5139 [0.000]
31 -0.3523 ** 0.0415 429.4696 [0.000]
32 -0.3182 ** 0.0264 455.1120 [0.000]
33 -0.2788 * 0.0197 478.7498 [0.000]
34 -0.2347 0.0275 499.6746 [0.000]
35 -0.1844 0.0433 516.9007 [0.000]
36 -0.1281 0.0571 529.3810 [0.000]
37 -0.0667 0.0543 536.1445 [0.000]
Performing iterative calculation of rho...
ITER RHO ESS
1 0.68440 3.30021e+010
2 0.72176 3.27194e+010
3 0.73325 3.26563e+010
4 0.73761 3.26352e+010
5 0.73938 3.26270e+010
6 0.74013 3.26237e+010
7 0.74044 3.26223e+010
8 0.74058 3.26217e+010
9 0.74063 3.26214e+010
10 0.74066 3.26213e+010
11 0.74067 3.26213e+010
12 0.74067 3.26213e+010
13 0.74068 3.26213e+010
14 0.74068 3.26213e+010
Model 5: Prais-Winsten, using observations 1980-2017 (T = 38)
Dependent variable: GDP
rho = 0.740676
coefficient std. error t-ratio p-value
---------------------------------------------------------
const −263258 42262.3 −6.229 3.44e-07 ***
CPI 16820.8 609.737 27.59 8.26e-026 ***
Statistics based on the rho-differenced data:
Sum squared resid 3.26e+10 S.E. of regression 30102.26
R-squared 0.995643 Adjusted R-squared 0.995522
F(1, 36) 541.6707 P-value(F) 2.74e-23
rho 0.037099 Durbin-Watson 1.854400
Statistics based on the original data:
Mean dependent var 787903.9 S.D. dependent var 440968.1
Performing iterative calculation of rho...
ITER RHO ESS
1 0.68440 2.98101e+010
2 0.66891 2.97947e+010
3 0.66844 2.97947e+010
4 0.66843 2.97947e+010
5 0.66843 2.97947e+010
Model 4: Cochrane-Orcutt, using observations 1981-2017 (T = 37)
Dependent variable: GDP
rho = 0.668427
coefficient std. error t-ratio p-value
---------------------------------------------------------
const −323831 42511.3 −7.618 6.21e-09 ***
CPI 17548.0 582.366 30.13 1.27e-026 ***
Statistics based on the rho-differenced data:
Sum squared resid 2.98e+10 S.E. of regression 29176.65
R-squared 0.995634 Adjusted R-squared 0.995509
F(1, 35) 907.9547 P-value(F) 1.27e-26
rho 0.122660 Durbin-Watson 1.679103
Statistics based on the original data:
Mean dependent var 804791.5 S.D. dependent var 434414.7
Model 9: OLS, using observations 1981-2017 (T = 37)
Dependent variable: Y
coefficient std. error t-ratio p-value
---------------------------------------------------------
const −102508 14155.2 −7.242 1.87e-08 ***
X 17560.6 611.776 28.70 6.49e-026 ***
Mean dependent var 279756.1 S.D. dependent var 142553.3
Sum squared resid 2.98e+10 S.E. of regression 29184.17
R-squared 0.959252 Adjusted R-squared 0.958088
F(1, 35) 823.9386 P-value(F) 6.49e-26
Log-likelihood −431.8838 Akaike criterion 867.7676
Schwarz criterion 870.9894 Hannan-Quinn 868.9035
rho 0.107090 Durbin-Watson 1.707324
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