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 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.
An I(d) process can be constructed by summing an I(d − 1) process:
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