Simulation smoothing for state-space models: A computational efficiency analysis

Simulation smoothing involves drawing state variables (or innovations) in discrete time state-space models from their conditional distribution given parameters and observations. Gaussian simulation smoothing is of particular interest, not only for the direct analysis of Gaussian linear models, but also for the indirect analysis of more general models. Several methods for Gaussian simulation smoothing exist, most of which are based on the Kalman filter. Since states in Gaussian linear state-space models are Gaussian Markov random fields, it is also possible to apply the Cholesky Factor Algorithm to draw states. This algorithm takes advantage of the band diagonal structure of the Hessian matrix of the log density to make efficient draws. We show how to exploit the special structure of state-space models to draw latent states even more efficiently. ∗Corresponding author. Mailing address: Département de sciences économiques, C.P. 6128, succursale Centre-ville, Montréal QC H3C 3J7, Canada. Telephone: (514) 343-7281. Fax: (514) 343-7221. e-mail: [email protected]. Web site: www.cirano.qc.ca/∼mccauslw. †Same mailing address as McCausland. e-mail: [email protected]. ‡Mailing address: Department of Economics, Campus Box 8110, North Carolina State University, Raleigh, 27695-8110, USA. e-mail: denis [email protected]. Web site: http://www4.ncsu.edu/∼dpellet.