Random central limit theorems for linear processes with weakly dependent innovations

Random central limit theorems (CLTs) are established for a linear process driven by a strictly stationary ψψ-weakly dependent process as well as for the ψψ-weakly dependent process itself, whose dependence structure was introduced by Doukhan and Louhichi [Doukhan, P., & Louhichi, S. (1999). A new weak dependence condition and applications to moment inequalities. Stochastic Processes and their Applications, 30 84, 313–342] to generalize mixings and other dependence. Random CLTs are established for partial sums and sample autocovariances of the ψψ-weakly dependent process and the linear process under absolute summability.