Moving Average Model
The notation MA(q) refers to the moving average model of order q:
where the θ1, ..., θq are
the parameters of the model, μ is the expectation of (often assumed to equal 0),
and the , ,... are white noise error terms. This can be equivalently written in terms of the backshift operator B as:
Thus, a moving-average model is conceptually a linear regression of the current value of the series against current and previous (unobserved) white noise error
terms or random shocks. The random shocks at each point are assumed to be mutually independent and to come from the same distribution, typically a normal distribution, with location at zero (MEAN) and constant scale (SD).