Given a time series process:
$$ Z(t)=(β−α)Z(t−1)−βZ(t−2)+e(t), t∈Z, $$
and
$$ X(t)−X(t-1)=β(X(t-1)−X(t−2))−α(X(t-1)−μ(t-1))+e(t-1), t∈Z $$
Show that Z(t) - Z(t-1) is a stationary process
Where Z(t) can be written as:
$$ Z(t)=X(t)−μt− \frac{(β−1)μ}{α} $$