Trend-stationary process
Stochastic process in time series analysis / From Wikipedia, the free encyclopedia
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In the statistical analysis of time series, a trend-stationary process is a stochastic process from which an underlying trend (function solely of time) can be removed, leaving a stationary process.[1] The trend does not have to be linear.
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Conversely, if the process requires differencing to be made stationary, then it is called difference stationary and possesses one or more unit roots.[2][3] Those two concepts may sometimes be confused, but 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. transitory, the time series will converge again towards the growing mean, which was not affected by the shock) while unit-root processes have a permanent impact on the mean (i.e. no convergence over time).[4]