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Here is the documentation for statsmodel's ARMA fit function. My issue is that it does not specify the form of the model it is fitting, i.e. is it fitting $a(L)y_t = b(L)\epsilon_t$ or is it fitting the regression form enter image description here

It's a bit confusing because statsmodel's ARMA generation assumes the form $a(L)y_t = b(L)\epsilon_t$, but the "no constant" option makes it unclear.

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  • $\begingroup$ Since the documentation says ARMA(p,q), I think it has the form that you describe. It has the option to include or exclude the constant c. $\endgroup$
    – Michael R. Chernick
    Commented Jan 12, 2017 at 0:40
  • $\begingroup$ I mean, both are ARMA(p,q), one is just more succinct than the other. $\endgroup$
    – user369210
    Commented Jan 12, 2017 at 0:41

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The "constant" option in the fit returns the mean, from which the actual constant can be recovered using $\mu = \beta_0/(1- \beta_1 - \cdots - \beta_p)$.

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  • $\begingroup$ Is this behavior documented? I couldn't find it on the package's website and spent days trying to figure out what the heck is going on. Thanks $\endgroup$
    – Confounded
    Commented Apr 3, 2020 at 13:18

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