Tempered fractionally integrated process with stable noise as a transient anomalous diffusion model

Tempered fractionally integrated process with stable noise as a transient anomalous diffusion model

We present here the autoregressive tempered fractionally integrated moving average (ARTFIMA) process obtained by taking the tempered fractional difference operator of the non-Gaussian stable noise. The tempering parameter makes the ARTFIMA process stationary for a wider range of the memory parameter...

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Bibliographic Details
Main Authors: Burnecki, K. (Author), Kabala, J. (Author), Sabzikar, F. (Author)
Format: Article
Language:English
Published: IOP Publishing Ltd 2022
Subjects:
codifference
stable distribution
tempered fractional calculus
Whittle method
Yaglom noise
Online Access:View Fulltext in Publisher
Description
Summary:We present here the autoregressive tempered fractionally integrated moving average (ARTFIMA) process obtained by taking the tempered fractional difference operator of the non-Gaussian stable noise. The tempering parameter makes the ARTFIMA process stationary for a wider range of the memory parameter values than for the classical autoregressive fractionally integrated moving average, and leads to semi-long range dependence and transient anomalous behavior. We investigate ARTFIMA dependence structure with stable noise and construct Whittle estimators. We also introduce the stable Yaglom noise as a continuous version of the ARTFIMA model with stable noise. Finally, we illustrate the usefulness of the ARTFIMA process on a trajectory from the Golding and Cox experiment. © 2022 The Author(s). Published by IOP Publishing Ltd.
ISBN:17518113 (ISSN)
DOI:10.1088/1751-8121/ac5b92

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