On Importance Sampling for State Space Models

Borus Jungbacker () and Siem Jan Koopman ()
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Borus Jungbacker: Vrije Universiteit Amsterdam

No 05-117/4, Tinbergen Institute Discussion Papers from Tinbergen Institute

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.

Keywords: Kalman filter; Likelihood function; Monte Carlo integration; Newton-Raphson; Posterior mode estimation; Simulation smoothing; Stochastic volatility model (search for similar items in EconPapers)
JEL-codes: C15 C32 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: Written
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Persistent link: http://EconPapers.repec.org/RePEc:dgr:uvatin:20050117

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