Order of integration

In statistics, the order of integration, denoted I(d), of a time series is a summary statistic, which reports the minimum number of differences required to obtain a covariance-stationary series.

A time series is integrated of order d if is a stationary process, where

is the lag operator and

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