An introduction to I(∞) processes

This paper presents an example of a time series model that is not difference stationary to any order and explores its properties. The process is dubbed I(∞). Although taking differences cannot make it stationary, there is a simple method of inducing stationarity. The result indicates that the popular notion of integratedness may be too linear. An extension to possible cointegrating relations among I(∞) processes is also discussed.