Bayesian inference for continuous-time ARMA models driven by non-Gaussian levy processes

In this paper we present methods for estimating the parameters of a class of non-Gaussian continuous-time stochastic process, the continuous-time autoregressive moving average (CARMA) model driven by symmetric alpha-Stable (S alpha S) Levy processes. In this challenging framework we are not able to evaluate the likelihood function directly, and instead we use a disctretized approximation to the likelihood. The parameters are then estimated from this approximating model using a Bayesian Monte Carlo scheme, and employing a Kalman filter to marginalize and sample the trajectory of the state process. An efficient exploration of the parameter space is achieved through a novel reparameterization in terms of an equivalent mechanical system. Simulations demonstrate the potential of the methods.