Strictly stationary solutions of ARMA equations in Banach spaces

Abstract

We obtain necessary and sufficient conditions for the existence of strictly stationary solutions of ARMA equations in Banach spaces with independent and identically distributed noise under certain assumptions. First, we obtain conditions for ARMA(1,$q$) equations by excluding zero and the unit circle from the spectrum of the operator of the AR part. We then extend this to ARMA($p$,$q$) equations. Finally, we discuss various examples.