Bayesian Inference for Continuous-Time ARMA Models Driven by Jump Diffusions

This paper investigates the problem of Bayesian parameter estimation for continuous-time autoregressive moving average (CARMA) models driven by jump diffusions. Inference is performed through the evaluation of the likelihood function conditional on jump times, and the realized jump sizes are marginalized assuming they are normally distributed. A Markov chain Monte Carlo (MCMC) algorithm is then developed to explore the parameter space based on the conditional likelihood and an assumed prior structure. Finally, simulations are provided to demonstrate the potential of our methods.