Monte Carlo Estimation for Nonlinear Non-Gaussian State Space Models |
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Authors: | Jungbacker Borus; Koopman Siem Jan |
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Institution: | Department of Econometrics, VU University Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands bjungbacker{at}feweb.vu.nl s.j.koopman{at}feweb.vu.nl |
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Abstract: | We develop a proposal or importance density for state spacemodels with a nonlinear non-Gaussian observation vector y p(y¦ )and an unobserved linear Gaussian signal vector p( ). The proposaldensity is obtained from the Laplace approximation of the smoothingdensity p( ¦y). We present efficient algorithms to calculatethe mode of p( ¦y) and to sample from the proposal density.The samples can be used for importance sampling and Markov chainMonte Carlo methods. The new results allow the application ofthese methods to state space models where the observation densityp(y¦ ) is not log-concave. Additional results are presentedthat lead to computationally efficient implementations. We illustratethe methods for the stochastic volatility model with leverage. |
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Keywords: | Importance sampling Kalman filtering Markov chain Monte Carlo Newton-Raphson Posterior mode Simulation smoothing Stochastic volatility model |
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