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Particle filtering approximations for a Gaussian-generalized inverse Gaussian model

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  • Ferrante, Marco
  • Frigo, Nadia

Abstract

We consider the filtering problem for a class of discrete-time partially observable stochastic processes. Under strong conditions on the parameters involved and on the initial condition, we are able to prove that it admits a finite dimensional filter. Relaxing these assumptions, we use a Rao Blackwellization procedure to perform a Particle filtering approximation of the filtering distribution, then we prove its convergence and extend this study to a jump Markov model.

Suggested Citation

  • Ferrante, Marco & Frigo, Nadia, 2009. "Particle filtering approximations for a Gaussian-generalized inverse Gaussian model," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 442-449, February.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:4:p:442-449
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    References listed on IDEAS

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    1. P. Vidoni, 1999. "Exponential family state space models based on a conjugate latent process," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 213-221.
    2. Ferrante, Marco & Vidoni, Paolo, 1998. "Finite dimensional filters for nonlinear stochastic difference equations with multiplicative noises," Stochastic Processes and their Applications, Elsevier, vol. 77(1), pages 69-81, September.
    3. Shephard, Neil, 1994. "Local scale models : State space alternative to integrated GARCH processes," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 181-202.
    4. Genon-Catalot, Valentine, 2003. "A non-linear explicit filter," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 145-154, January.
    5. Ferrante, Marco & Vidoni, Paolo, 1999. "A Gaussian-generalized inverse Gaussian finite-dimensional filter," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 165-176, November.
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