Algorithms for testing of fractional dynamics: a practical guide to ARFIMA modelling

K Burnecki, A Weron - Journal of Statistical Mechanics: Theory …, 2014 - iopscience.iop.org
In this survey paper we present a systematic methodology which demonstrates how to
identify the origins of fractional dynamics. We consider three mechanisms which lead to it …

Estimating the anomalous diffusion exponent for single particle tracking data with measurement errors-An alternative approach

K Burnecki, E Kepten, Y Garini, G Sikora, A Weron - Scientific reports, 2015 - nature.com
Accurately characterizing the anomalous diffusion of a tracer particle has become a central
issue in biophysics. However, measurement errors raise difficulty in the characterization of …

Energy demand forecasting using adaptive ARFIMA based on a novel dynamic structural break detection framework

A Nikseresht, H Amindavar - Applied Energy, 2024 - Elsevier
Forecasting energy demand has become increasingly important due to technological
advances, especially new power systems and population growth. Accurate predictions of …

Hourly solar irradiance forecasting based on statistical methods and a stochastic modeling approach for residual error compensation

A Nikseresht, H Amindavar - Stochastic Environmental Research and Risk …, 2023 - Springer
By reducing fossil fuel use, renewable energy improves the economy, quality of life, and
environment. These impacts make renewable energy forecasting crucial for lowering fossil …

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

F Sabzikar, J Kabala, K Burnecki - Journal of Physics A …, 2022 - iopscience.iop.org
We present here the autoregressive tempered fractionally integrated moving average
(ARTFIMA) process obtained by taking the tempered fractional difference operator of the non …

Identification and validation of stable ARFIMA processes with application to UMTS data

K Burnecki, G Sikora - Chaos, Solitons & Fractals, 2017 - Elsevier
In this paper we present an identification and validation scheme for stable autoregressive
fractionally integrated moving average (ARFIMA) time series. The identification part relies on …

Identifying diffusive motions in single-particle trajectories on the plasma membrane via fractional time-series models

K Burnecki, G Sikora, A Weron, MM Tamkun, D Krapf - Physical Review E, 2019 - APS
In this paper we show that an autoregressive fractionally integrated moving average time-
series model can identify two types of motion of membrane proteins on the surface of …

Modeling of water usage by means of ARFIMA–GARCH processes

J Gajda, G Bartnicki, K Burnecki - Physica A: Statistical Mechanics and its …, 2018 - Elsevier
This paper addresses an important problem of modeling and prediction of phenomena with
antipersistent behavior and variance changing in time. As a proper stochastic model we …

Systematic inference of the long-range dependence and heavy-tail distribution parameters of ARFIMA models

T Graves, CLE Franzke, NW Watkins… - Physica A: statistical …, 2017 - Elsevier
Abstract Long-Range Dependence (LRD) and heavy-tailed distributions are ubiquitous in
natural and socio-economic data. Such data can be self-similar whereby both LRD and …

Solar X-ray variability in terms of a fractional heteroskedastic time series model

AA Stanislavsky, K Burnecki, J Janczura… - Monthly Notices of …, 2019 - academic.oup.com
The Sun is variable in activity with changes on time-scales as short as minutes to as long as
a solar cycle. Although the most accurate measurements are limited to the satellite era, the …