The Lévy State Space Model

• DOI: 10.48550/arxiv.1912.12524
• Publication Date: 2019-01-01
• Authors: Simon Godsill; Marina Riabiz; Ioannis Kontoyiannis
• Keywords: State-space representation; Similarity (geometry)

In this paper we introduce a new class of state space models based on shot-noise simulation representations non-Gaussian L\'evy-driven linear systems, represented as stochastic differential equations. particular conditionally Gaussian version the is proposed that able to capture heavy-tailed non-Gaussianity while retaining tractability for inference procedures. We focus canonical such processes, $\alpha$-stable L\'evy which retain important properties self-similarity and heavy-tails, emphasizing broader classes processes may be handled by similar methodology. An feature are marginalise both skewness scale parameters these challenging from posterior probability distributions. The posed in continuous time so deal with irregular data arrival times. Example modelling procedures provided using Rao-Blackwellised sequential Monte Carlo applied two-dimensional Langevin model, tested real exchange rate data.