Systematic inference of the long-range dependence and heavy-tail distribution parameters of ARFIMA models
Systematic inference of the long-range dependence and heavy-tail distribution parameters of ARFIMA models
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DOI：
10.1016/j.physa.2017.01.028
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发表时间：
2017-05-01
影响因子：
3.3
通讯作者：
Tindale, Elizabeth
中科院分区：
文献类型：
--
作者：
Graves, Timothy;Franzke, Christian L. E.;Tindale, Elizabeth
长程相关（LRD）和重尾分布在自然和社会经济数据中普遍存在。这样的数据可以是自相似的，由此LRD和重尾分布都有助于通过赫斯特指数测量的自相似性。物理科学中广泛使用的一些方法分别估计这两个参数，这可能会导致估计偏差。那些做同时估计的是基于频率论的方法，如惠特尔近似最大似然估计。在这里，我们提出了一个新的和系统的贝叶斯框架的LRD和重尾分布参数的参数ARFIMA模型的非高斯新息的同时推断。作为创新，我们使用了具有幂律尾部的a-稳定分布和t-分布。我们的算法还提供了参数的不确定性估计。我们测试我们的算法使用合成数据，也从地球同步业务环境卫星系统（GOES）的太阳X射线时间序列的数据。这些测试表明，我们的算法能够准确和鲁棒地估计LRD和重尾分布参数。(C)2017爱思唯尔B. V.保留所有权利。
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 heavy-tailed distributions contribute to the self-similarity as measured by the Hurst exponent. Some methods widely used in the physical sciences separately estimate these two parameters, which can lead to estimation bias. Those which do simultaneous estimation are based on frequentist methods such as Whittle's approximate maximum likelihood estimator. Here we present a new and systematic Bayesian framework for the simultaneous inference of the LRD and heavy-tailed distribution parameters of a parametric ARFIMA model with non-Gaussian innovations. As innovations we use the a-stable and t-distributions which have power law tails. Our algorithm also provides parameter uncertainty estimates. We test our algorithm using synthetic data, and also data from the Geostationary Operational Environmental Satellite system (GOES) solar X-ray time series. These tests show that our algorithm is able to accurately and robustly estimate the LRD and heavy-tailed distribution parameters. (C) 2017 Elsevier B.V. All rights reserved.