A method of deriving asymptotics for linear processes is introduced which uses an explicit algebraic decomposition of the linear ﬁlter. The method leads to substantial simpliﬁcations in the asymptotics and oﬀers a uniﬁed approach to strong laws and central limit theory for linear processes. Sample means and sample covariances are covered. The results also accommodate both homogeneous and heterogeneous innovations as well as innovations with undeﬁned means and variances.
Phillips, Peter C.B. and Solo, Victor, "Asymptotics for Linear Processes" (1989). Cowles Foundation Discussion Papers. 1175.