TY  - JOUR
A1  - Gairing, Jan M.
A1  - Hogele, Michael A.
A1  - Kosenkova, Tania
A1  - Monahan, Adam H.
T1  - How close are time series to power tail Levy diffusions?
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - 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 a-stable Levy 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. Published by AIP Publishing.
Y1  - 2017
U6  - https://doi.org/10.1063/1.4986496
SN  - 1054-1500
SN  - 1089-7682
VL  - 27
PB  - American Institute of Physics
CY  - Melville
ER  -