Examples
Some well-known special cases arise naturally. For example, an ARIMA(0,1,0) model is given by:
which is simply a random walk.
A number of variations on the ARIMA model are commonly used. For example, if multiple time series are used then the can be thought of as vectors and a VARIMA model may be appropriate. Sometimes a seasonal effect is suspected in the model. For example, consider a model of daily road traffic volumes. Weekends clearly exhibit different behaviour from weekdays. In this case it is often considered better to use a SARIMA (seasonal ARIMA) model than to increase the order of the AR or MA parts of the model. If the time-series is suspected to exhibit long-range dependence then the parameter may be replaced by certain non-integer values in an autoregressive fractionally integrated moving average model, which is also called a Fractional ARIMA (FARIMA or ARFIMA) model.
Read more about this topic: Autoregressive Integrated Moving Average
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