Other Special Forms
The explicit identification of the factorisation of the autoregression polynomial into factors as above, can be extended to other cases, firstly to apply to the moving average polynomial and secondly to include other special factors. For example, having a factor in a model is one way of including a non-stationary seasonality of period s into the model. Another example is the factor, which includes a (non-stationary) seasonality of period 12. The effect of the first type of factor is to allow each season's value to drift separately over time, whereas with the second type values for adjacent seasons move together.
Identification and specification of appropriate factors in an ARIMA model can be an important step in modelling as it can allow a reduction in the overall number of parameters to be estimated, while allowing the imposition on the model of types of behaviour that logic and experience suggest should be there.
Read more about this topic: Autoregressive Integrated Moving Average
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