The Lévy State Space Model
The Lévy State Space Model
复制标题
Lévy 状态空间模型
DOI：
10.1109/ieeeconf44664.2019.9048715
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Ioannis Kontoyiannis
中科院分区：
文献类型：
--
作者：
S. Godsill;M. Riabiz;Ioannis Kontoyiannis
在本文中，我们引入了一类新的状态空间模型，该模型基于非高斯 Lévy 驱动线性系统的散粒噪声模拟表示，表示为随机微分方程。特别是提出了模型的条件高斯版本，它能够捕获重尾非高斯性，同时保留推理过程的易处理性。我们关注此类过程的典型类别，即 α-稳定 Lévy 过程，它保留了自相似性和重尾等重要属性，同时强调更广泛类别的非高斯 Lévy 过程可以通过类似的方法来处理。一个重要的特征是，我们能够从后验概率分布中边缘化这些具有挑战性的模型的偏度和尺度参数。这些模型是在连续时间内建立的，因此能够处理不规则的数据到达时间。使用应用于二维 Langevin 模型的 Rao-Blackwellized 顺序蒙特卡罗提供了示例建模和推理过程，并在实际汇率数据上进行了测试。
In this paper we introduce a new class of state space models based on shot-noise simulation representations of nonGaussian Lévy-driven linear systems, represented as stochastic differential equations. In particular a conditionally Gaussian version of the models is proposed that is able to capture heavy-tailed non-Gaussianity while retaining tractability for inference procedures. We focus on a canonical class of such processes, the α-stable Lévy processes, which retain important properties such as self-similarity and heavy-tails, while emphasizing that broader classes of non-Gaussian Lévy processes may be handled by similar methodology. An important feature is that we are able to marginalise both the skewness and the scale parameters of these challenging models from posterior probability distributions. The models are posed in continuous time and so are able to deal with irregular data arrival times. Example modelling and inference procedures are provided using Rao-Blackwellised sequential Monte Carlo applied to a two-dimensional Langevin model, and this is tested on real exchange rate data.
影响因子：
2.4
作者：
José M Bernardo and Adrian F M Smith-José-M-Bernardo-and-Adrian-F-M-Smith-2177748935
通讯作者：
José M Bernardo and Adrian F M Smith-José-M-Bernardo-and-Adrian-F-M-Smith-2177748935