Complete q -order moment convergence of moving average processes under ϕ -mixing assumptions

Xing-Cai Zhou; Jin-Guan Lin

Applications of Mathematics (2014)

  • Volume: 59, Issue: 1, page 69-83
  • ISSN: 0862-7940

Abstract

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Let { Y i , - ∞ < i < ∞ } be a doubly infinite sequence of identically distributed ϕ -mixing random variables, and { a i , - ∞ < i < ∞ } an absolutely summable sequence of real numbers. We prove the complete q -order moment convergence for the partial sums of moving average processes X n = ∑ i = - ∞ ∞ a i Y i + n , n ≥ 1 based on the sequence { Y i , - ∞ < i < ∞ } of ϕ -mixing random variables under some suitable conditions. These results generalize and complement earlier results.

How to cite

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Zhou, Xing-Cai, and Lin, Jin-Guan. "Complete $q$-order moment convergence of moving average processes under $\varphi $-mixing assumptions." Applications of Mathematics 59.1 (2014): 69-83. <http://eudml.org/doc/260809>.

@article{Zhou2014,
abstract = {Let $\lbrace Y_i, -\infty <i<\infty \rbrace $ be a doubly infinite sequence of identically distributed $\varphi $-mixing random variables, and $\lbrace a_i, -\infty <i<\infty \rbrace $ an absolutely summable sequence of real numbers. We prove the complete $q$-order moment convergence for the partial sums of moving average processes $\Big \lbrace X_n=\sum _\{i=-\infty \}^\infty a_i Y_\{i+n\},n\ge 1\Big \rbrace $ based on the sequence $\lbrace Y_i, -\infty <i<\infty \rbrace $ of $\varphi $-mixing random variables under some suitable conditions. These results generalize and complement earlier results.},
author = {Zhou, Xing-Cai, Lin, Jin-Guan},
journal = {Applications of Mathematics},
keywords = {moving average; $\varphi $-mixing; complete convergence; $q$-order moment; maximum of partial sums; -order complete convergence; moving average process; maximum of partial sums; -mixing},
language = {eng},
number = {1},
pages = {69-83},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Complete $q$-order moment convergence of moving average processes under $\varphi $-mixing assumptions},
url = {http://eudml.org/doc/260809},
volume = {59},
year = {2014},
}

TY - JOUR
AU - Zhou, Xing-Cai
AU - Lin, Jin-Guan
TI - Complete $q$-order moment convergence of moving average processes under $\varphi $-mixing assumptions
JO - Applications of Mathematics
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 1
SP - 69
EP - 83
AB - Let $\lbrace Y_i, -\infty <i<\infty \rbrace $ be a doubly infinite sequence of identically distributed $\varphi $-mixing random variables, and $\lbrace a_i, -\infty <i<\infty \rbrace $ an absolutely summable sequence of real numbers. We prove the complete $q$-order moment convergence for the partial sums of moving average processes $\Big \lbrace X_n=\sum _{i=-\infty }^\infty a_i Y_{i+n},n\ge 1\Big \rbrace $ based on the sequence $\lbrace Y_i, -\infty <i<\infty \rbrace $ of $\varphi $-mixing random variables under some suitable conditions. These results generalize and complement earlier results.
LA - eng
KW - moving average; $\varphi $-mixing; complete convergence; $q$-order moment; maximum of partial sums; -order complete convergence; moving average process; maximum of partial sums; -mixing
UR - http://eudml.org/doc/260809
ER -

References

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