Title :
Bayesian Inference for Continuous-Time Arma Models Driven by Non-Gaussian L É VY Processes
Author :
Godsill, S.J. ; Yang, G.
Author_Institution :
Dept. of Eng., Cambridge Univ.
Abstract :
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
Keywords :
Bayes methods; Kalman filters; Monte Carlo methods; approximation theory; autoregressive moving average processes; matrix algebra; Bayesian Monte Carlo scheme; Bayesian inference; Kalman filter; continuous-time ARMA models; continuous-time auto regressive moving average; continuous-time stochastic process; nonGaussian Levy processes; symmetric alpha-stable Levy processes; Autoregressive processes; Bayesian methods; Differential equations; Laboratories; Mechanical systems; Monte Carlo methods; Parameter estimation; Signal processing; State estimation; Stochastic processes;
Conference_Titel :
Acoustics, Speech and Signal Processing, 2006. ICASSP 2006 Proceedings. 2006 IEEE International Conference on
Conference_Location :
Toulouse
Print_ISBN :
1-4244-0469-X
DOI :
10.1109/ICASSP.2006.1661347