Random central limit theorems (CLTs) are established for a linear process driven by a strictly stationary ψ-weakly dependent process as well as for the ψ-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 ψ-weakly dependent process and the linear process under absolute summability.
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The authors are very grateful for constructive and valuable comments of two anonymous referees. This work was supported partly by the Priority Research Centers Program ( 2009-0093827 ), and partly by the Basic Research Program ( 2010-0023000 ) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education Science and Technology.
- Linear process
- Random central limit theorem
- Sample covariance
- Weak dependence