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A Gaussian-generalized inverse Gaussian finite-dimensional filter

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  • Ferrante, Marco
  • Vidoni, Paolo

Abstract

We consider the filtering problem for a partially observable stochastic process , solution to a nonlinear system of stochastic difference equations, which provides a stochastic modellization for both the mean and the variance of the Gaussian observation distribution. The noises in the equations are given by two sequences of independent Gaussian random variables and a sequence of independent gamma random variables. We are able to prove that there exists a finite-dimensional filter system for this model, since, for each n, the conditional distribution of (Xn,Zn) given (Y0,...,Yn) is that of a suitable bivariate Gaussian-generalized inverse Gaussian random variable.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:84:y:1999:i:1:p:165-176
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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.
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    Cited by:

    1. 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.

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