How close are time series to power tail Lévy diffusions?

This article presents a new and easily implementable method to quantify the so-called coupling distance between the law of a time series and the law of a differential equation driven by Markovian additive jump noise with heavy-tailed jumps, such as α-stable Lévy flights. Coupling distances measure t...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2017-07, Vol.27 (7), p.073112-073112
Main Authors: Gairing, Jan M., Högele, Michael A., Kosenkova, Tania, Monahan, Adam H.
Format: Article
Language:English
Subjects:
Computer simulation
Coupling
Differential equations
Markov processes
Time series
Upper bounds
Water vapor
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Summary:This article presents a new and easily implementable method to quantify the so-called coupling distance between the law of a time series and the law of a differential equation driven by Markovian additive jump noise with heavy-tailed jumps, such as α-stable Lévy flights. Coupling distances measure the proximity of the empirical law of the tails of the jump increments and a given power law distribution. In particular, they yield an upper bound for the distance of the respective laws on path space. We prove rates of convergence comparable to the rates of the central limit theorem which are confirmed by numerical simulations. Our method applied to a paleoclimate time series of glacial climate variability confirms its heavy tail behavior. In addition, this approach gives evidence for heavy tails in datasets of precipitable water vapor of the Western Tropical Pacific.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.4986496