i get that you have to find the roots of the characteristic polynomial but can someone explain the intuition behind the roots must be outside the unit circle? what is a unit circle?
before anyone downvotes me saying theres another similar discussion, i have read it and i dont understand what it means for roots to lie outside a unit circle.
Here is a simple answer:
An AR process is like a linear recurrence relation with some noise.
The asymptotical comportement of the sequence depend on the roots of the defining polynome as the general form of the solution of a linear recurence is a sum of basis solutions:
$a_{i}*r_{i}^{n}$
where $r_{i}$ is a root of the defining polynome, $a_{i}$ constants.
$r_{i}$ can be a complex number, written as $r = A *e^{i\theta}$.
So $r^{n} = A^{n}*e^{in\theta}$.
As we have $ |e^{in\theta}| = 1 $, $ |r^{n}| = |A|^{n} $
So if $|A|>1$ the solution will diverge. So if $|A|<1$ the solution will dtend to 0. So if $|A|=1$ the solution will oscillate.
If you represent r in the complexe plane, you can see that the circle centered in 0 of radius 1 play an important role. $|A|>1$ (resp. $|A|<1$ resp. $|A|=1$) correspond to outside the circle (resp. inside, resp. on). It's called the unit circle. (see: http://en.wikipedia.org/wiki/Unit_circle).
It's not easy to go from linear recurence to AR process, but the idea for the asymptotical comportement is here. The behavior of the process differs depending on how the roots of the polynom are positionned towrds the units circle.
Check out this article. It has the most simple and elaborate discussion of what exactly is happening in ARIMA Model. https://towardsdatascience.com/unboxing-arima-models-1dc09d2746f8
Basically, these parameters tell you how the time series is progressing.
