Algorithms for testing of fractional dynamics: a practical guide to ARFIMA modelling
Algorithms for testing of fractional dynamics: a practical guide to ARFIMA modelling
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DOI：
10.1088/1742-5468/2014/10/p10036
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发表时间：
2014-10-01
影响因子：
2.4
通讯作者：
Weron, Aleksander
中科院分区：
文献类型：
--
作者：
Burnecki, Krzysztof;Weron, Aleksander
在这篇调查论文中，我们提出了一种系统方法论，展示了如何识别分数动力学的起源。我们考虑导致它的三种机制，即分数布朗运动、分数列维稳定运动和自回归分数积分移动平均（ARFIMA）过程，但我们专注于 ARFIMA 建模。该方法基于用于识别和验证分数动力学的统计工具，特别是 ARFIMA 参数估计器、遍历性测试、基于样本 p 变化的自相似指数估计器和基于样本均方位移的记忆参数估计器。附录 A-F 中提供了所需算法的完整列表。最后，我们说明了各种经验数据的方法，并表明 ARFIMA 可以被视为分数动力学的通用模型。因此，我们为实验者提供了如何有效地使用 ARFIMA 建模来处理大量异常扩散数据的实用指南。
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, namely fractional Brownian motion, fractional Levy stable motion and an autoregressive fractionally integrated moving average (ARFIMA) process but we concentrate on the ARFIMA modelling. The methodology is based on statistical tools for identification and validation of the fractional dynamics, in particular on an ARFIMA parameter estimator, an ergodicity test, a self-similarity index estimator based on sample p-variation and a memory parameter estimator based on sample mean-squared displacement. A complete list of algorithms needed for this is provided in appendices A-F Finally, we illustrate the methodology on various empirical data and show that ARFIMA can be considered as a universal model for fractional dynamics. Thus, we provide a practical guide for experimentalists on how to efficiently use ARFIMA modelling for a large class of anomalous diffusion data.