\begin{definition}[Definition:Moving Average Model/Parameter]
Let $S$ be a stochastic process based on an equispaced time series.
Let the values of $S$ at timestamps $t, t - 1, t - 2, \dotsc$ be $z_t, z_{t - 1}, z_{t - 2}, \dotsc$
Let $\tilde z_t$ be the deviation from a constant mean level $\mu$:
:$\tilde z_t = z_t - \mu$
Let $a_t, a_{t - 1}, a_{t - 2}, \dotsc$ be a sequence of independent shocks at timestamps $t, t - 1, t - 2, \dotsc$
Let $M$ be an '''moving average model''' on $S$ of order $q$:
:$\tilde z_t = a_t - \theta_1 a_{t - 1} - \theta_2 a_{t - 2} - \dotsb - \theta_q a_{t - q}$
The '''parameters''' of $M$ consist of:
:the constant mean level $\mu$
:the variance $\sigma_a^2$ of the underlying (usually white noise) process of the independent shocks $a_t$
:the coefficients $\theta_1$ to $\theta_q$.
In practice, each of these '''parameters''' needs to be estimated from the data.
\end{definition}