进行ARIMA分析时，Stata 17的输出和statsmodels的输出不同
我申请的时候
re = ARIMA(df_log, order = (0,1,2))
print(re`.fit().summary())
the results were as follows
SARIMAX Results
==============================================================================
Dep. Variable: GDP No. Observations: 62
Model: ARIMA(0, 1, 2) Log Likelihood 48.459
Date: Thu, 11 May 2023 AIC -90.918
Time: 02:21:08 BIC -84.585
Sample: 01-01-1960 HQIC -88.436
- 01-01-2021
Covariance Type: opg
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
ma.L1 0.4751 0.142 3.349 0.001 0.197 0.753
ma.L2 -0.0500 0.151 -0.332 0.740 -0.345 0.245
sigma2 0.0119 0.002 6.720 0.000 0.008 0.015
===================================================================================
Ljung-Box (L1) (Q): 4.11 Jarque-Bera (JB): 3.62
Prob(Q): 0.04 Prob(JB): 0.16
Heteroskedasticity (H): 0.60 Skew: 0.37
Prob(H) (two-sided): 0.27 Kurtosis: 3.94
===================================================================================
然而，当在 Stata 17 中执行相同的方法时，相同数据的结果如下
arima log_gdp, arima(0,1,2)(setting optimization to BHHH)
Iteration 0: log likelihood = 51.833406
Iteration 1: log likelihood = 58.219464
Iteration 2: log likelihood = 59.750732
Iteration 3: log likelihood = 60.128641
Iteration 4: log likelihood = 60.183567
(switching optimization to BFGS)
Iteration 5: log likelihood = 60.191613
Iteration 6: log likelihood = 60.192693
Iteration 7: log likelihood = 60.192721
Iteration 8: log likelihood = 60.192721
ARIMA regression
Sample: 1961 thru 2021 Number of obs = 61
Wald chi2(2) = 17.21
Log likelihood = 60.19272 Prob > chi2 = 0.0002
------------------------------------------------------------------------------
| OPG
D.log_gdp | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
log_gdp |
_cons | .0707899 .0085723 8.26 0.000 .0539885 .0875912
-------------+----------------------------------------------------------------
ARMA |
ma |
L1. | .1135653 .103465 1.10 0.272 -.0892223 .3163529
L2. | -.4008123 .1129969 -3.55 0.000 -.6222821 -.1793425
-------------+----------------------------------------------------------------
/sigma | .0899162 .007283 12.35 0.000 .0756417 .1041907
------------------------------------------------------------------------------
Note: The test of the variance against zero is one sided, and the two-sided
confidence interval is truncated at zero.
结果不同。因此，如果我遗漏了什么，请寻求解释。尽管如此，如果我在 statsmodels 中使用级别 1 的差异数据，但模型 = ARIMA(0,0,2)，结果是匹配的。这里我使用的是 statsmodels verison 0.13.5
re = ARIMA(df_log.diff().dropna(), order = (0,1,2))`
print(re.fit().summary()`
SARIMAX Results
==============================================================================
Dep. Variable: GDP No. Observations: 61
Model: ARIMA(0, 0, 2) Log Likelihood 60.193
Date: Thu, 11 May 2023 AIC -112.386
Time: 02:14:30 BIC -103.942
Sample: 01-01-1961 HQIC -109.076
- 01-01-2021
Covariance Type: opg
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0708 0.009 8.258 0.000 0.054 0.088
ma.L1 0.1136 0.103 1.098 0.272 -0.089 0.316
ma.L2 -0.4008 0.113 -3.548 0.000 -0.622 -0.179
sigma2 0.0081 0.001 6.174 0.000 0.006 0.011
===================================================================================
Ljung-Box (L1) (Q): 0.00 Jarque-Bera (JB): 2.57
Prob(Q): 0.99 Prob(JB): 0.28
Heteroskedasticity (H): 0.60 Skew: 0.36
Prob(H) (two-sided): 0.26 Kurtosis: 3.71
===================================================================================