DeepAI AI Chat
Log In Sign Up

The Lévy State Space Model

by   Simon Godsill, et al.
University of Cambridge
King's College London

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


page 1

page 2

page 3

page 4


Generalised Hyperbolic State-space Models for Inference in Dynamic Systems

In this work we study linear vector stochastic differential equation (SD...

Generalised shot noise representations of stochastic systems driven by non-Gaussian Lévy processes

We consider the problem of obtaining effective representations for the s...

A General Class of Score-Driven Smoothers

Motivated by the observation that score-driven models can be viewed as a...

Controlling the flexibility of non-Gaussian processes through shrinkage priors

The normal inverse Gaussian (NIG) and generalized asymmetric Laplace (GA...

Structured Variational Inference in Unstable Gaussian Process State Space Models

Gaussian processes are expressive, non-parametric statistical models tha...

Nested Gaussian filters for recursive Bayesian inference and nonlinear tracking in state space models

We introduce a new sequential methodology to calibrate the fixed paramet...

An introduction to state-space modeling of ecological time series

State-space models (SSMs) are an important modeling framework for analyz...