Causality and invertibility root criteria for an ARMA model

For a minimal ARMA representation $\varphi (B)X=\theta (B)ϵ$, causality requires every zero of $\varphi$ to lie strictly outside the unit disk, and invertibility requires the same of $\theta$. This makes the transfer function and its reciprocal analytic on a disk larger than the unit disk, giving geometrically decreasing one-sided filter coefficients. Cancel common factors before applying the criterion to the noise-driven representation.