Bayesian Inference for Continuous-Time Arma Models Driven by Non-Gaussian L É VY Processes

In this paper we present methods for estimating the parameters of a class of non-Gaussian continuous-time stochastic process, the continuous-time auto regressive moving average (CARMA) model driven by symmetric alpha-stable (SalphaS) Levy processes. In this challenging framework we are not able to evaluate the likelihood function directly, and instead we use a distretized 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