In time series analysis, the moving-average (MA) model is a common approach for modeling univariate time series. The moving-average model specifies that the output variable depends linearly on the current and various past values of a stochastic (imperfectly predictable) term.

$\{X_t\}$ is a Moving Average Process of order $q$, MA($q$), if we can write

$$X_t = Z_t + \theta_1Z_{t-1} + \dots + \theta_qZ_{t-q},$$

where $Z_t \sim N(0,\sigma^2)$ and $\theta_i$'s are scalars.

  • $X_t$ is a linear combination of i.i.d. mean 0 random variables
  • $X_t$ can also be thought of as a weighted sum of the past $q$ forecast errors and a contemporanous error term.