Order of integration
In statistics, the order of integration, denoted I, of a time series is a summary statistic, which reports the minimum number of differences required to obtain a covariance-stationary series.
The order of integration is a key concept in time series analysis, particularly when dealing with non-stationary data that exhibits trends or other forms of non-stationarity.
Integration of order ''d''
A time series is integrated of order d ifis a stationary process, where is the lag operator and is the first difference, i.e.
In other words, a process is integrated to order d if taking repeated differences d times yields a stationary process.
In particular, if a series is integrated of order 0, then is stationary.