Template-Type: ReDIF-Paper 1.0 Series: Tinbergen Institute Discussion Papers Creation-Date: 2005-12-19 Number: 05-117/4 Author-Name: Borus Jungbacker Author-Email: bjungbacker@feweb.vu.nl Author-Workplace-Name: Vrije Universiteit Amsterdam Author-Name: Siem Jan Koopman Author-Email: s.j.koopman@feweb.vu.nl Author-Workplace-Name: Vrije Universiteit Amsterdam Title: On Importance Sampling for State Space Models Abstract: 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. Classification-JEL: C15; C32 Keywords: Kalman filter; Likelihood function; Monte Carlo integration; Newton-Raphson; Posterior mode estimation; Simulation smoothing; Stochastic volatility model File-Url: https://papers.tinbergen.nl/05117.pdf File-Format: application/pdf File-Size: 265136 bytes Handle: RePEc:tin:wpaper:20050117