Imagine we have two time-series processes, which are stable, producing: $x_t,y_t$.

Is $z_t=\alpha x_t +\beta y_t$, $\forall \alpha, \beta \in \mathbb{R}$ also stable?

Any help would be appreciated.

I would say yes, since it has an MA representation.

Imagine we have two time-series processes, which are stationary, producing: $x_t,y_t$.

Is $z_t=\alpha x_t +\beta y_t$, $\forall \alpha, \beta \in \mathbb{R}$ also stationary?

Any help would be appreciated.

I would say yes, since it has an MA representation.