 Invertibility of a moving-average model

Invertibility permits reconstruction of innovations from present and past observations by a stable filter. For $Y_t-\mu ={\epsilon }_t+\theta {\epsilon }_{t-1}$, $|\theta |<1$ gives ${\epsilon }_t={\sum }_{j\ge 0}(-\theta {)}^j(Y_{t-j}-\mu )$. This is a different property from stationarity: a finite moving-average model is stationary for every finite coefficient.