6. Integrated ARMA processes

The two main characteristics of the time series developed in the previous chapter, ARMAs, are (in addition to their zero mean, which we have assumed essentially because the general method of studying time series begins, among other things, by suppressing the mean value), stationarity and short memory (i.e. exponential decay).

We will now study integrated ARMA processes, which do not simultaneously exhibit these two properties:

• ARIMA (Autoregressive Integrated Moving Average) processes are non-stationary;

• ARFIMA (Autoregressive Fractionaly Integrated Moving Average) processes are stationary, with long memory.