@inproceedings{
kindap2023generalised,
title={Generalised Hyperbolic State-space Models for Inference in Dynamic Systems},
author={Yaman Kindap and Simon J. Godsill},
booktitle={NeurIPS 2023 Workshop Heavy Tails in Machine Learning},
year={2023},
url={https://openreview.net/forum?id=9xNDQJER95}
}
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.
Generalised Hyperbolic State-space Models for Inference in Dynamic Systems
Yaman Kindap Simon J. Godsill