I am quite new to time series analysis and I am delving for the first time into stationary processes. I don't seem to understand the concepts of non-stationarity and the presence of roots within the unit circle. Particularly, these are my questions:
Where does the characteristic equation come from (i.e. what is its meaning) and why is it important? (I know the way it is built, I just do not understand why it is built that way)
Why can we say that a process is stationary if and only if the roots of the characteristic equation are outside of the unit circle?