%0 Journal Article
%T The functional AR(1) process with a unit root
%A Nelson Muriel
%J Statistics
%D 2015
%I arXiv
%X We define strong and weak unit roots for the functional AR(1) process and give some theoretical examples. It is shown that a functional form of cointegration occurs in which only a finite number of common trends exist. Using functional Principal Component Analysis we illustrate the presence of functional unit roots in two demographic data sets. We close with some remarks concerning our assumptions and the possibility of generalizing our results.
%U http://arxiv.org/abs/1512.01844v1