Why Distinguish Between Trend Stationary and Difference Stationary Processes

Abstract

This chapter provides some motivation for the continued interest in assessing whether a stochastic process has a unit root, particularly for series that exhibit trended behaviour. In part, such interest lies in a critique of a procedure that models the trend component of a series as a deterministic function of time, usually as a simple low-order polynomial of time, a linear trend being a common choice. In essence, such a procedure is not meant to be taken as a structural explanation of the systematic movement in a series, but rather as a workable proxy for a large number of forces that could be reduced to a simple representation. In the case of some time series this view seems to find support in the data, perhaps more so with slowly moving trended series such as population than with more erratic series such as the prices of financial assets. Deviations from the trend are then viewed as transitory, the trend being the attractor to which the series reverts given sufficient time for adjustment. This, of course, is the trend stationary view of the generation of time series.