The MA model specifies that the output variable depends linearly on the past and current past values of a stochastic term (imperfectly predictable). The MA model should not be confused with the MA we have seen in the previous sections. This is an essentially different concept although some similarities are evident. Unlike the AR model, the finished MA model is always stationary.

Just as a model AR (p) regresses with respect to the past values of the series, an MA (q) model uses past errors as explanatory variables.

The MA model of q order is defined as:

In the previous formula, the terms are defined as follows:

• Y_t is the actual value at time period t
• μ is the mean of the series
• θ_i (i = 1,2,..., q) are model parameters
• ε_t-i is the past random error at time period t-i
• ε_t is the random error at time period t (white noise)

The MA model is essentially a finite impulsive response filter applied to white noise, with some additional interpretations placed on it.