On Importance Sampling for State Space Models
VU University Amsterdam - Department of Economics
Siem Jan Koopman
VU University Amsterdam; Tinbergen Institute
Tinbergen Institute Discussion Paper No. 05-117
We consider likelihood inference and state estimation by means of importance sampling for state space models with a nonlinear non-Gaussian observation y ~ p(y|alpha) and a linear Gaussian state alpha ~ p(alpha). The importance density is chosen to be the Laplace approximation of the smoothing density p(alpha|y). We show that computationally efficient state space methods can be used to perform all necessary computations in all situations. It requires new derivations of the Kalman filter and smoother and the simulation smoother which do not rely on a linear Gaussian observation equation. Furthermore, results are presented that lead to a more effective implementation of importance sampling for state space models. An illustration is given for the stochastic volatility model with leverage.
Number of Pages in PDF File: 28
Keywords: Kalman filter, Likelihood function, Monte Carlo integration, Newton-Raphson, Posterior mode estimation, Simulation smoothing, Stochastic volatility model
JEL Classification: C15, C32working papers series
Date posted: January 3, 2006
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