Generalised Hyperbolic State-Space Models for Inference in Dynamic Systems
Abstract
In this work we study linear vector stochastic differential equation (SDE) models driven by the generalised hyperbolic (GH) L{\'e}vy process for inference in continuous-time non-Gaussian filtering problems. The GH family of stochastic processes offers a flexible framework for modelling of non-Gaussian, heavy-tailed characteristics and includes the normal inverse-Gaussian, variance-gamma and Student-t processes as special cases. We present continuous-time simulation methods for the solution of vector SDE models driven by GH processes and novel inference methodologies using a variant of sequential Markov chain Monte Carlo (MCMC). As an example a particular formulation of Langevin dynamics is studied within this framework. The model is applied to both a synthetically generated data set and a real-world financial series to demonstrate its capabilities.
Cite
Text
Kindap and Godsill. "Generalised Hyperbolic State-Space Models for Inference in Dynamic Systems." NeurIPS 2023 Workshops: HeavyTails, 2023.Markdown
[Kindap and Godsill. "Generalised Hyperbolic State-Space Models for Inference in Dynamic Systems." NeurIPS 2023 Workshops: HeavyTails, 2023.](https://mlanthology.org/neuripsw/2023/kindap2023neuripsw-generalised/)BibTeX
@inproceedings{kindap2023neuripsw-generalised,
title = {{Generalised Hyperbolic State-Space Models for Inference in Dynamic Systems}},
author = {Kindap, Yaman and Godsill, Simon J.},
booktitle = {NeurIPS 2023 Workshops: HeavyTails},
year = {2023},
url = {https://mlanthology.org/neuripsw/2023/kindap2023neuripsw-generalised/}
}