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Workshop: Heavy Tails in ML: Structure, Stability, Dynamics

Generalised Hyperbolic State-space Models for Inference in Dynamic Systems

Yaman Kindap · Simon Godsill

Keywords: [ stochastic differential equations ] [ Levy processes ] [ sequential MCMC ] [ Continuous-time filtering ] [ non-linear filtering ]


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.

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