The last type of process used in ARIMA models, and the most difficult to visualize, is
the moving average. In a moving-average process, each value is determined by the average of the current disturbance and one or more previous disturbances. The order of the
moving average process specifies how many previous disturbances are averaged into the
new value. The equation for a first-order moving average process is:
In the standard notation, an MA(n) or ARIMA(0,0,n) process uses n previous disturbances along with the current one.
The difference between an autoregressive process and a moving-average process is
subtle but important. Each value in a moving-average series is a weighted average of the
most recent random disturbances, while each value in an autoregression is a weighted
average of the recent values of the series. Since these values in turn are weighted averages of the previous ones, the effect of a given disturbance in an autoregressive process
dwindles as time passes. In a moving-average process, a disturbance affects the system
for a finite number of periods (the order of the moving average) and then abruptly ceases
to affect it.