Ergodicity testing using an analytical formula for a dynamical functional of alpha-stable autoregressive fractionally integrated moving average processes

Hanna Loch, Joanna Janczura, and Aleksander Weron
Phys. Rev. E 93, 043317 – Published 19 April 2016

Abstract

In this paper we study asymptotic behavior of a dynamical functional for an α-stable autoregressive fractionally integrated moving average (ARFIMA) process. We find an analytical formula for this important statistics and show its usefulness as a diagnostic tool for ergodic properties. The obtained results point to the very fast convergence of the dynamical functional and show that even for short trajectories one may obtain reliable conclusions on the ergodic properties of the ARFIMA process. Moreover we use the obtained theoretical results to illustrate how the dynamical functional statistics can be used in the verification of the proper model for an analysis of some biophysical experimental data.

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  • Received 15 December 2015
  • Revised 18 February 2016

DOI:https://doi.org/10.1103/PhysRevE.93.043317

©2016 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Hanna Loch

  • Faculty of Pure & Applied Mathematics, Wrocław University of Science and Technology, 50-370 Wrocław, Poland

Joanna Janczura and Aleksander Weron

  • Faculty of Pure & Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, 50-370 Wrocław, Poland

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Issue

Vol. 93, Iss. 4 — April 2016

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