Detrending Time Series: A Cautionary Note

Trends in time series may produce spurious covariation among variables. Although it is clearly necessary to model such sources of covariation, it is equally necessary to model those processes correctly. This article considers two types of processes that produce trends in time series. Trend stationary processes produce a constant rate of change in the level of a variable. Difference stationary processes produce a random rate of change in the level of a variable. Methods to detrend time series presuppose one or the other of these two basic processes. Tests to distinguish trend stationary from difference stationary processes are described and illustrated. It is shown that choice of method makes a difference and that the consequences of incorrectly detrending time series may be severe.