CUED Publications database

The Lévy State Space Model

Godsill, S and Riabiz, M and Kontoyiannis, I (2019) The Lévy State Space Model. Conference Record - Asilomar Conference on Signals, Systems and Computers, 2019-N. pp. 487-494. ISSN 1058-6393

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Abstract

© 2019 IEEE. 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.

Item Type: Article
Uncontrolled Keywords: math.PR math.PR cs.IT math.IT stat.ME
Subjects: UNSPECIFIED
Divisions: Div F > Signal Processing and Communications
Depositing User: Cron Job
Date Deposited: 08 Jan 2020 20:01
Last Modified: 25 Aug 2020 01:29
DOI: 10.1109/IEEECONF44664.2019.9048715