# How does Python's statsmodel ARMA fit work?

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

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.

• 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. – Michael Chernick Jan 12 '17 at 0:40
• I mean, both are ARMA(p,q), one is just more succinct than the other. – user369210 Jan 12 '17 at 0:41

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