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Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State Space Models


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  • Siem Jan Koopman

    (VU University Amsterdam)

  • Andre Lucas

    (VU University Amsterdam)

  • Marcel Scharth

    (VU University Amsterdam)


We introduce a new efficient importance sampler for nonlinear non-Gaussian state space models. We propose a general and efficient likelihood evaluation method for this class of models via the combination of numerical and Monte Carlo integration methods. Our methodology explores the idea that only a small part of the likelihood evaluation problem requires simulation. We refer to our new method as numerically accelerated importance sampling. The method is computationally and numerically efficient, facilitates parameter estimation for models with high-dimensional state vectors, and overcomes a bias-variance trade-off encountered by other sampling methods. An elaborate simulation study and an empirical application for U.S. stock returns reveal large efficiency gains for a range of models used in financial econometrics.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 11-057/4.

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Date of creation: 22 Mar 2011
Date of revision: 27 Jan 2012
Handle: RePEc:dgr:uvatin:20110057

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Keywords: State space models; importance sampling; simulated maximum likelihood; stochastic volatility; stochastic copula; stochastic conditional duration;

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Cited by:
  1. Siem Jan Koopman & Geert Mesters, 2014. "Empirical Bayes Methods for Dynamic Factor Models," Tinbergen Institute Discussion Papers, Tinbergen Institute 14-061/III, Tinbergen Institute.
  2. Siem Jan Koopman & Marcel Scharth, 2011. "The Analysis of Stochastic Volatility in the Presence of Daily Realised Measures," Tinbergen Institute Discussion Papers, Tinbergen Institute 11-132/4, Tinbergen Institute.
  3. Geert Mesters & Siem Jan Koopman, 2012. "Generalized Dynamic Panel Data Models with Random Effects for Cross-Section and Time," Tinbergen Institute Discussion Papers, Tinbergen Institute 12-009/4, Tinbergen Institute, revised 18 Mar 2014.
  4. Siem Jan Koopman & Andre Lucas & Marcel Scharth, 2012. "Predicting Time-Varying Parameters with Parameter-Driven and Observation-Driven Models," Tinbergen Institute Discussion Papers, Tinbergen Institute 12-020/4, Tinbergen Institute.
  5. Siem Jan Koopman & Rutger Lit & André Lucas, 2014. "The Dynamic Skellam Model with Applications," Tinbergen Institute Discussion Papers, Tinbergen Institute 14-032/IV/DSF73, Tinbergen Institute.


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