ARIMA stands for AutoRegressive Integrated Moving Average.

The ARIMA Time Series Analysis uses lags and shifts in the historical data to uncover patterns (e.g. moving averages, seasonality) and predict the future. The ARIMA model was first developed in the late 60s but it was systemized by Box and Jenkins in 1976. ARIMA can be more complex to use than other statistical forecasting techniques, although when implemented properly ARIMA can be quite powerful and flexible.

ARIMA is a method for determining two things:

1. How much of the past should be used to predict the next observation (length of weights)

2. The values of the weights.

For example y(t)= 1/3 * y(t-3) + 1/3 * y(t-2) + 1/3 * y(t-1) is an ARIMA model; another ARIMA MODEL is y(t)= 1/6 * y(t-3) + 4/6 * y(t-2) + 1/6 * y(t-1)

Thus the correct ARIMA model requires identification of the right number of lags and the coefficients that should be used.
ARIMA model identification uses autoregressions to identify the underling model.
Care must be taken to robustly identify and estimate parameters as outliers (pulses, level shifts , local time trends ) can wreak havoc.