Topological crackle of heavy-tailed moving average processes

Takashi Owada

Stochastic Processes and their Applications, 2019, vol. 129, issue 12, 4965-4997

Abstract: The main focus of this paper is topological crackle, the layered structure of annuli formed by heavy-tailed random points in Rd. In view of extreme value theory, we study the topological crackle generated by a heavy-tailed discrete-time moving average process. Because of the clustering effect of a moving average process, various topological cycles are produced consecutively in time in the layers of the crackle. We establish the limit theorems for the Betti numbers, a basic quantifier of topological cycles. The Betti number converges to the sum of stochastic integrals, some of which induce multiple cycles because of the clustering effect.

Keywords: Extreme value theory; Random topology; Topological crackle; Moving average process; Betti number (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:12:p:4965-4997

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DOI: 10.1016/j.spa.2018.12.017

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