Ljung-box test using fixed lag value of 1 in ARIMA model

Start with the linked test_serial_correlation implementation in statsmodels/tsa/statespace/mlemodel.py and compare its lag choice with acorr_ljungbox and the ARIMA model summary. Trace how nobs_diffuse is used and determine whether the differing Ljung–Box results are expected; done means the lag and nobs_diffuse behavior is clearly explained or corrected.

I am using an ARIMA model to predict the time series values. I identify the best fit ARIMA model using the AIC value and it turns out that for all the different orders that I tried, the best AIC is returned for the ARIMA order (4, 0, 1).

As I am using statsmodels.tsa.arima.model.ARIMA package, I could see the description of the fitted model using model.summary() and I could observe the following results for tests:

===================================================================================
Ljung-Box (L1) (Q):                   0.00   Jarque-Bera (JB):              4412.50
Prob(Q):                              0.99   Prob(JB):                         0.00
Heteroskedasticity (H):               5.21   Skew:                            -0.01
Prob(H) (two-sided):                  0.00   Kurtosis:                        12.17
===================================================================================

I also manually ran the test using the statsmodels.stats.diagnostic.acorr_ljungbox and statsmodels.stats.stattools.jarque_bera packages respectively. I am using the following code snippet for the same:

jbTest = jarque_bera(model.resid)
print("JBTest:", jbTest)
lbTest = acorr_ljungbox(model.resid, model_df=p_+q_, lags=[20], boxpierce=False)
print("LBTest:", lbTest)

where, model is my best-fit ARIMA model and p_ and q_ are the respective orders of the model. The output from the snippet:

JBTest: (4412.481863170613, 0.0, -0.008442090306796898, 12.171354626003195)
LBTest: (array([32.85885778]), array([0.00490945]))

I can observe that the Jarque-Bera test output is close to the approximations from the model. However, it looks like the Ljunge-box test output is significantly small and does not match with the output from model. I am not sure if I am mis-interpreting the output from the model description versus the output from the acorr_ljungbox function.

However, when I changed my code to use lbTest = acorr_ljungbox(model.resid, lags=[1], boxpierce=False) instead of above snippet, I got values very close to the estimates from the model: LBTest: (array([0.000103]), array([0.9919025])). I did not understand why we are using the lag=1 as found in the class here.

Also, I am confused about the theoretical understanding of the nobs_diffuse value used in the test_serial_correlation function in same class. Any pointers would be really helpful!

I am using statsmodels version 0.12.2.