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Markov chain Monte Carlo methods for switching diffusion models. (English) Zbl 0984.62060
Summary: 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.

##### MSC:
 62M05 Markov processes: estimation; hidden Markov models 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62P05 Applications of statistics to actuarial sciences and financial mathematics 65C40 Numerical analysis or methods applied to Markov chains
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