When is an altoregressive scheme stationary

Abstract

We show that a sufficient condition for an autoregrassive scheme to be stationary is that the roots of the indicia1 polynomial lie within the unit circle. The importance of this theorem is that its proof yields some interesting results. The main ones are: (i) when fitting an autoregressive scheme via the Yule-Walker equations, the fitted scheme is guaranteed to be stationary, and (ii) an easily applicable test to check whether a given scheme is stationary or not is found.