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Ergodicity testing using an analytical formula for a dynamical functional of alpha-stable autoregressive fractionally
Hanna Loch1, Joanna Janczura2, Aleksander Weron2
1Faculty of Pure & Applied Mathematics, Wrocław University of Science and Technology, 50-370 Wrocław, Poland.
Physical Review. E
|May 14, 2016
Summary
This study presents a formula for the asymptotic behavior of a dynamical functional in alpha-stable ARFIMA processes. The findings demonstrate its rapid convergence and utility in assessing ergodic properties, even with limited data.
Area of Science:
- Statistics
- Time Series Analysis
- Dynamical Systems
Background:
- Autoregressive Fractionally Integrated Moving Average (ARFIMA) processes are widely used in time series analysis.
- Understanding the asymptotic behavior of functionals is crucial for statistical inference.
- Alpha-stable distributions offer a more flexible framework than Gaussian distributions for modeling heavy-tailed data.
Purpose of the Study:
- To derive an analytical formula for the asymptotic behavior of a dynamical functional for alpha-stable ARFIMA processes.
- To establish the utility of this dynamical functional as a diagnostic tool for ergodic properties.
- To demonstrate the application of these theoretical results in analyzing biophysical experimental data.
Main Methods:
- Derivation of an analytical formula for the asymptotic behavior of the dynamical functional.
- Analysis of the convergence properties of the dynamical functional.
- Application of the dynamical functional for model verification in biophysical data analysis.
Main Results:
- An analytical formula for the asymptotic behavior of the dynamical functional was successfully derived.
- The dynamical functional exhibits very fast convergence.
- The results indicate that reliable conclusions on ergodic properties can be obtained even from short time series trajectories.
Conclusions:
- The derived analytical formula provides a valuable tool for understanding alpha-stable ARFIMA processes.
- The fast convergence of the dynamical functional allows for efficient assessment of ergodic properties.
- The study highlights the practical applicability of dynamical functional statistics in biophysical data analysis for model verification.
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