Markov chain Monte Carlo methods for switching diffusion models

Reversible jump Metropolis–Hastings updating schemes can be used to analyse continuous‐time latent models, sometimes known as state space models or hidden Markov models. We consider models where the observed process X can be represented as a stochastic differential equation and where the latent process D is a continuous‐time Markov chain. We develop Markov chain Monte Carlo methods for analysing both Markov and non‐Markov versions of these models. As an illustration of how these methods can be used in practice we analyse data from the New York Mercantile Exchange oil market. In addition, we analyse data generated by a process that has linear and mean reverting states.