We can achieve similar results with Autoregressive Integrated Moving Average (ARIMA) models. To predict future values of a time-series, we usually have to stationarize it first, which means that the data has a constant mean, variance, and autocorrelation over time. In the past two sections, we used seasonal decomposition and the Holt-Winters filter to achieve this. Now let's see how the generalized version of the Autoregressive Moving Average (ARMA) model can help with this data transformation.
ARIMA(p, d, q) actually includes three models with three non-negative integer parameters:
p refers to the autoregressive part of the model
d refers to the integrated part
q refers to the moving average parts
As ARIMA also includes an integrated (differencing) part over ARMA, it can deal with non-stationary time-series as well, as they naturally become stationary after differencing—in other words, when the d parameter is larger than zero.
Traditionally...