Unit root

Article summary

In probability theory and statistics, a unit root is a property of certain stochastic processes (such as a random walk) that can create challenges for statistical inference in time series models. A linear stochastic process contains a unit root if 1 is a solution to its characteristic equation. Processes with a unit root are non-stationary, because they do not necessarily exhibit a deterministic trend. If the other roots of the characteristic equation lie inside the unit circle—that is, have a modulus (absolute value) less than one—then the first difference of the process will be stationary; otherwise, the process will need to be differenced multiple times to become stationary. If there are d unit roots, the process will have to be differenced d times in order to make it stationary. Due to this characteristic, unit root processes are also called difference stationary. Unit root processes may sometimes be confused with trend-stationary processes; while they share many properties, they are different in many aspects. It is possible for a time series to be non-stationary, yet have no unit root and be trend-stationary. In both unit root and trend-stationary processes, the mean can be growing or decreasing over time; however, in the presence of a shock, trend-stationary processes are mean-reverting (i.e.…

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