This is a pretty simple question but didn't find anything relevant here, so hope it's not a duplicate.

I've used statsmodels python library to find the best parameters (minimizing the AIC) for an ARIMA model and the result of the fitting with such parameters set [(1,1,1)x(1,1,0,12)] on the data is:

Model fit result

Now, while that model will minimize the AIC value, I see some coefficients with p-values that indicate non statistical significance (ar1 with 0.966 and ar.S with 0.543). What does that mean? Should I set those coefficients to 0 or the corresponding parameters and refit the model?

Any hint or clarification is greatly appreciated.

Thank you

  • $\begingroup$ 2) Yes, you can. 1) I means that your library couldn't work with incomplete polynoms and fit all $\phi / \theta$ values of characteristic polynomials. $\endgroup$
    – Dmitriy
    Commented May 7, 2019 at 16:00
  • $\begingroup$ sorry Dmitriy, could you elaborate more on that? Also, would you suggest alternative libraries? Thanks $\endgroup$
    – crash
    Commented May 7, 2019 at 17:38
  • $\begingroup$ Unfortunately, I can recommend only R libraries. So, I think your library should support fixed values for $\phi / \theta$ parameters. $\endgroup$
    – Dmitriy
    Commented May 7, 2019 at 17:41

1 Answer 1


There's no rule that says p-values have to be significant. Your fit/estimator is the best one (in the sense of AIC/likelihood) regardless of what the p-values are (there's a big general controversy going on in statistics and areas where statistics is applied about sense, nonsense and rampant overinterpretation of p-values in general). So there is no reason to set parameters to zero.

An insignificant p-value in fact means that, assuming that all the other parameters are still in the model and general model assumptions hold, a model with that particular parameter set to zero is compatible with the data. This doesn't mean that the parameter is in fact zero; the value that you estimated is also compatible with the data and still better in the sense of AIC. The p-value is relevant if it is your research aim to make statements about whether that term is required, or if for some reason you want to get rid of certain parameters (in which case some people think that there are better options than using the p-value). However if you just want a good fit or a model that gives good predictions, use the fit you got and don't worry about p-values.


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