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A non-linear explicit filter

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  • Genon-Catalot, Valentine

Abstract

We propose a non-linear model of filtering in discrete time. The signal is linear but noises are multiplicative and non-Gaussian. We exhibit a class of distributions including the standard centered Gaussian which is closed for the filtering algorithm.

Suggested Citation

  • Genon-Catalot, Valentine, 2003. "A non-linear explicit filter," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 145-154, January.
    • Handle: RePEc:eee:stapro:v:61:y:2003:i:2:p:145-154
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    References listed on IDEAS

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    1. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    2. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
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    Cited by:

    1. Kon Kam King, Guillaume & Pandolfi, Andrea & Piretto, Marco & Ruggiero, Matteo, 2024. "Approximate filtering via discrete dual processes," Stochastic Processes and their Applications, Elsevier, vol. 168(C).
    2. Chaleyat-Maurel, Mireille & Genon-Catalot, Valentine, 2006. "Computable infinite-dimensional filters with applications to discretized diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1447-1467, October.
    3. Genon-Catalot, Valentine & Laredo, Catherine, 2006. "Leroux's method for general hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 222-243, February.
    4. Fabienne Comte & Valentine Genon-Catalot & Mathieu Kessler, 2011. "Multiplicative Kalman filtering," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 389-411, August.
    5. 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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