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We define strong and weak unit roots for the functional AR(1) process andgive some theoretical examples. It is shown that a functional form ofcointegration occurs in which only a finite number of common trends exist.Using functional Principal Component Analysis we illustrate the presence offunctional unit roots in two demographic data sets. We close with some remarksconcerning our assumptions and the possibility of generalizing our results.

The functional AR(1) process with a unit root