Generalised Hyperbolic State-space Models for Inference in Dynamic Systems

Published: 23 Oct 2023, Last Modified: 13 Nov 2023HeavyTails 2023EveryoneRevisionsBibTeX
Keywords: Continuous-time filtering, non-linear filtering, stochastic differential equations, sequential MCMC, Levy processes
TL;DR: Simulation and inference methods for stochastic differential equations driven by a generalised hyperbolic process
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.
Submission Number: 14