Estimating parameters of functional ARMA, GARCH and invertible processes requires estimating lagged covariance and cross‐covariance operators of Cartesian product Hilbert space‐valued processes. Asymptotic results have been derived in recent years, either less generally or under a strict...

In this paper we re-visit a recent theoretical idea introduced by Phillips and Lee (2015). They examine an empirically relevant situation when multiple time series under consideration exhibit different degrees of non-stationarity. By bridging the asymptotic theory of the local to unity and...