For context, I've been reading a text on time series analysis (on which I am comfortable with the statistics).
However, upon one example concerning the stability of an autoregressive process, the author solves for the polynomial roots from the characteristic equation by placing the characteristic equation in factored form.
Below, would someone please indicate the steps taken to get from the characteristic equation to the factor form?
Would be massively appreciated if someone could run through it, and fill in a knowledge gap of mine.
The AR process is given:
$y_t= 0.75y_{t-1}-0.125_{yt-2}+u_t$
The characteristic equation is given:
$1-0.75L+0.125L^2=0$
Which in factored form is given:
$(1-0.5L)(1-.25L)$
Many thanks to all concerned,
Best
Andrew