I think that the recurrence relation below is non-stationary as the coefficient 1.8 > 1 which seems to be one of the recurring conditions I've seen for the AR(1) model stationarity.
$x_t = 1.8 * x_{t-1} + w_t$
But I don't quite know how to explain why this is the case. I re-wrote the equation as $(1-1.8B)x_t = w_t$ where $B$ is the backwards operator and then I obtained the characteristic equation $1-1.8z = 0$ for some variable $z$ and I wasn't 100% sure from here as I understand that for it to be stationary the unit roots must be outside the circle and the characteristic root $z^* = 1/p_1$ is stationary then only if $|p_1| < 1$ but in my case $z^* = 1/1.8$ and $|p_1| > 1$
so is that enough to conclude that this recurrence relation is non-stationary?