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On Importance Sampling for State Space Models

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Author Info
Borus Jungbacker () (Vrije Universiteit Amsterdam)
Siem Jan Koopman () (Vrije Universiteit Amsterdam)

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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.

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Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 05-117/4.

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Date of creation: 19 Dec 2005
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Handle: RePEc:dgr:uvatin:20050117

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Web page: http://www.tinbergen.nl/

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Related research
Keywords: Kalman filter; Likelihood function; Monte Carlo integration; Newton-Raphson; Posterior mode estimation; Simulation smoothing; Stochastic volatility model;

Find related papers by JEL classification:
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November. [Downloadable!] (restricted)
  2. Michael K Pitt & Neil Shephard, . "Filtering via simulation: auxiliary particle filters," Economics Papers 1997-W13, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  3. Danielsson, J & Richard, J-F, 1993. "Accelerated Gaussian Importance Sampler with Application to Dynamic Latent Variable Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S153-73, Suppl. De. [Downloadable!] (restricted)
  4. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  5. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January. [Downloadable!] (restricted)
  6. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Oxford University Press for Biometrika Trust, vol. 89(3), pages 603-616, August.
  7. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August. [Downloadable!] (restricted)
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  1. Charles S. Bos & Phillip Gould, 2007. "Dynamic Correlations and Optimal Hedge Ratios," Tinbergen Institute Discussion Papers 07-025/4, Tinbergen Institute. [Downloadable!]
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