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Type: Journal article
Title: Functional limit theorem for moving average processes generated by dependent random variables
Author: Lin, Z.
Li, D.
Citation: Progress in Natural Science: communication of state key laboratories of China, 2006; 16(3):266-273
Publisher: Taylor & Francis Ltd
Issue Date: 2006
ISSN: 1002-0071
Statement of
Lin Zhengyan, Li Degui
Abstract: Let {Xt,t≥1} be a moving average process defined byXt = ∞∑j=0bjξt-j , where {bj,j≥0} is a sequence of real numbers and {ξt, ∞< t <∞} is a doubly infinite sequence of strictly stationary φ- mixing random variables. Under conditions on {bj, j ≥0}which entail that {Xt, t ≥ 1} is either a long memory process or a linear process, we study asymptotics of Sn ( s ) = [ns]∑t=1 Xt (properly normalized). When {Xt, t≥1} is a long memory process, we establish a functional limit theorem. When {Xt, t≥1} is a linear process, we not only obtain the multi-dimensional weak convergence for {Xt, t≥1}, but also weaken the moment condition on {ξt, - ∞< t <∞} and the restriction on {bj,j≥0}. Finally, we give some applications of our results.
Keywords: functional limit theorem
long memory process
linear process
moving average process
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