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Marcinkiewicz Strong Law of Large Numbers for Products of Long Range Dependent and Heavy Tailed Linear Processes
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- Author / Creator
- Paul, Sounak
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Classical methods of inference are often rendered inapplicable while dealing with data exhibiting heavy tails, which gives rise to infinite variance and frequent extremes, and long memory, which induces inertia in the data. In this thesis, we develop the Marcinkiewicz Strong Law of Large Numbers for products of two-sided univariate linear processes, with i.i.d. innovations which have zero mean and finite variance. The decay of the coefficients of these linear processes can be slow enough that the processes have long memory, while their innovations can have heavy tails. The aim of this thesis is to handle long-range dependence and heavy tails simultaneously, and to prove a decoupling property that shows the convergence rate of a Marcinkiewicz Strong Law in this setting, is dictated by the worst of long-range dependence and heavy tails, but not their combination.
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- Graduation date
- Fall 2019
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- Type of Item
- Thesis
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- Degree
- Master of Science
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- License
- Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.