Integrated, Unit Roots and Box-Jenkins Approach

The Box-Jenkins Approach is only valid if the variable being modeled is stationary. Although there are many different ways in which data can be nonstationary, Box and Jenkins assumed that the nature of economic time series data is such that any nonstationarity can be removed by differencing. This explains why, the Box-Jenkins approach deals mainly with differenced data.
A key ingredient of their methodology, an ingredient adopted by econometricians (without any justification based on economic theory), is their assumption that the nonstationarity is such that differencing will create stationarity. this concept is what is meant by the term Integrated : a variable is said to be integrated of order d, written I(d), if it must be differenced d times to be made stationary. Thus a stationary variable is integrated of order zero, written I(0), a variable which must be differenced once to become stationary is said to be I(1), integrated of order one, and so on. Economic variables are seldom integrated of order greater than two, and if nonstationary are usually I(1). Here is an I(1) random walk illustrative example given by Peter Kennedy: