In time series, a non-stationary process whose first difference is stationary, also referred to as an integrated of order one or (1)-process. An example of a unit root process is a random walk. The name ‘unit root’ is related to the roots of the polynomial equation derived from the lag polynomial representation of an autoregressive process:
A(L)yt = εt.
The process yt is stationary if all roots of equation A(z) = 0 exceed 1 in absolute value, and is non-stationary if at least one root is less than or equal to 1 in absolute value; the latter is called a unit root.