I'm currently taking a course in time-series at the undergraduate level. The course content goes right to the characteristic polynomial function (and solving it like you solve for roots) to determine if certain processes (e.g AR, MA, etc) is stationary or invertible.
After doing some googling it seems that many text-books go straight to the characteristic polynomial without explaining much. The professor did explain that to understand why, it requires a much higher level understanding than the undergraduate level.
What is it? Can we understand it intuitively without the complicated math?