Invertibility of a moving-average model
= Invertibility of a moving-average model
Invertibility permits reconstruction of innovations from present and past observations by a stable filter. For $Y_t-\mu=\varepsilon_t+\theta\varepsilon_{t-1}$, $|\theta|<1$ gives $\varepsilon_t=\sum_{j\ge0}(-\theta)^j(Y_{t-j}-\mu)$. This is a different property from stationarity: a finite moving-average model is stationary for every finite coefficient.