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Simulated Maximum Likelihood in Nonlinear Continuous-Discrete State Space Models: Importance Sampling by Approximate Smoothing

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  • Hermann Singer

    (FernUniversität Hagen)

Abstract

Summary The likelihood function of a continuous-discrete state space model is computed recursively by Monte Carlo integration, using importance sampling techniques. A functional integral representation of the transition density is utilized and importance densities are obtained by smoothing. Examples are the likelihood surfaces of an AR(2) process, a Ginzburg-Landau model and stock price models with stochastic volatilities.

Suggested Citation

  • Hermann Singer, 2003. "Simulated Maximum Likelihood in Nonlinear Continuous-Discrete State Space Models: Importance Sampling by Approximate Smoothing," Computational Statistics, Springer, vol. 18(1), pages 79-106, March.
    • Handle: RePEc:spr:compst:v:18:y:2003:i:1:d:10.1007_s001800300133
    DOI: 10.1007/s001800300133
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    References listed on IDEAS

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    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
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    6. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(4), pages 419-438, December.
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    Cited by:

    1. Hermann Singer, 2014. "Importance sampling for Kolmogorov backward equations," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(4), pages 345-369, October.

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