Abstract
Let \( {{\left( {{\xi_n}} \right)}_{{n\in \mathbb{Z}}}} \) be a stationary sequence of real random variables with E ξ 0 = 0 and infinite variance. Furthermore, assume that \( {{\left( {{c_n}} \right)}_{{n\in \mathbb{Z}}}} \) is a sequence of real numbers and \( {X_n}=\sum {_{{j\in \mathbb{Z}}}{c_j}{\xi_{n-j }}} \) is a moving average processes driven by \( {{\left( {{\xi_n}} \right)}_{{n\in \mathbb{Z}}}} \). By using a decomposition of the moving average processes, a central limit theorem for the partial sums \( \sum\nolimits_{k=1}^n {{X_k}} \) is established. As applications, we obtain some central limit theorems for stationary dependent sequences \( {{\left( {{\xi_n}} \right)}_{{n\in \mathbb{Z}}}} \), such as associated sequence, martingale difference, and so on.
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*This work is supported by NSFC (11001077, 11171093), NCET (NCET-11-0945), the Henan Province Foundation and Frontier Technology Research Plan (112300410205), and the Plan for Scientific Innovation Talent of Henan Province (124100510014).
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Miao, Y., Ge, L. & Xu, S. Central limit theorems for moving average processes* . Lith Math J 53, 80–90 (2013). https://doi.org/10.1007/s10986-013-9195-7
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DOI: https://doi.org/10.1007/s10986-013-9195-7