title: Ergodicity testing using an analytical formula for a dynamical functional of alpha-stable autoregressive fractionally integrated moving average processes.
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.
authors.affiliation: Faculty of Pure & Applied Mathematics, Wrocław University of Science and Technology, 50-370 Wrocław, Poland.
authors.forename: Hanna
authors.initials: H
authors.lastname: Loch
authors.affiliation: Faculty of Pure & Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, 50-370 Wrocław, Poland.
authors.forename: Joanna
authors.initials: J
authors.lastname: Janczura
authors.affiliation: Faculty of Pure & Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, 50-370 Wrocław, Poland.
authors.forename: Aleksander
authors.initials: A
authors.lastname: Weron