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On Importance Sampling for State Space Models

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  • Borus Jungbacker

    ()
    (Vrije Universiteit Amsterdam)

  • Siem Jan Koopman

    ()
    (Vrije Universiteit Amsterdam)

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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Bibliographic Info

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

Related research

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

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References

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  1. 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.
  2. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  3. Jun Yu, 2004. "On Leverage in a Stochastic Volatility Model," Econometric Society 2004 Far Eastern Meetings 506, Econometric Society.
  4. Neil Shephard & Michael K Pitt, 1995. "Likelihood analysis of non-Gaussian parameter driven models," Economics Papers 15 & 108., Economics Group, Nuffield College, University of Oxford.
  5. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543, September.
  6. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers 2005-W17, University of Oxford, Department of Economics.
  7. 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.
  8. Michael K Pitt & Neil Shephard, . "Filtering via simulation: auxiliary particle filters," Economics Papers 1997-W13, Economics Group, Nuffield College, University of Oxford.
  9. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
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Cited by:
  1. Charles S. Bos & Phillip Gould, 2007. "Dynamic Correlations and Optimal Hedge Ratios," Tinbergen Institute Discussion Papers 07-025/4, Tinbergen Institute.

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