Python ARIMA output - interpreting Sigma2

Question

I am trying to interpret ARIMA output below and not clear about sigma2. The documentation says it is 'The variance of the residuals.'. What is the hypothesis behind this output/importance?.

Kindly provide answer or a link where it is covered in detail.

import statsmodels.api as sm
mod = sm.tsa.statespace.SARIMAX(df.Sales, order=(0, 1, 1), 
seasonal_order=(0, 1, 1, 12), enforce_stationarity=False,
                            enforce_invertibility=False)
results = mod.fit()
print(results.summary().tables[1])



   ==============================================================================
                     coef    std err          z      P>|z|      [0.025      0.975]
    ------------------------------------------------------------------------------
    ma.L1         -0.9317      0.055    -16.989      0.000      -1.039      -0.824
    ma.S.L12      -0.0851      0.143     -0.594      0.553      -0.366       0.196
    sigma2      1.185e+09   2.13e-11   5.56e+19      0.000    1.19e+09    1.19e+09
    ==============================================================================

score 2 · Accepted Answer · answered Oct 18 '20 at 07:37

Yes, you're right that sigma squared represents the variance of the residual values. This value is used to test the normality of residuals against the alternative of non-normality.

For more information, you can check this PR: https://github.com/statsmodels/statsmodels/pull/2431

and this QA: https://github.com/statsmodels/statsmodels/issues/2507#:~:text=The%20sigma2%20output%20in%20the,variance%20of%20the%20error%20term.

Python ARIMA output - interpreting Sigma2

1 Answers1