Abstract
We study complete convergence and closely related Hsu–Robbins–Erdős-Spitzer–Baum–Katz series for sums whose terms are elements of linear autoregression sequences. We obtain criteria for convergence of these series expressed in terms of moment assumptions, which for “weakly dependent” sequences are the same as in classical results concerning the independent case.
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The author would like to thank the referee for careful reading and valuable suggestions.
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Supported by the Grant 0118U003614 from Ministry of Education and Science of Ukraine (project N 2105\(\phi\)).
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Ilienko, M. On the convergence of the Baum--Katz series for elements of a linear autoregression. Acta Math. Hungar. 164, 413–427 (2021). https://doi.org/10.1007/s10474-021-01157-3
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DOI: https://doi.org/10.1007/s10474-021-01157-3
Key words and phrases
- linear autoregression model
- weighted sum
- complete convergence
- Hsu–Robbins–Erdős series
- Spitzer series
- Baum–Katz series