# What are the properties of invertible Moving Average

If $X_t$ is an invertible MA(q) process $$X_t = Z_t + \theta_1 Z_{t-1} + \cdots + \theta_q Z_{t-q}$$ where $\{Z_t\} \sim \text{IID}(0,\sigma^2)$, and $EZ_t^4 < \infty$, then the parameter estimates from an innovations algorithm are asymptotically normal. For more details, check out "Applications of Innovation Representations in Time Series Analysis" by Brockwell and Davis (1988).