Multiplicative Kalman filtering

• Autores: Fabienne Comte, Valentine Genon Catalot, Mathieu Kessler
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 20, Nº. 2, 2011, págs. 389-411
• Idioma: inglés
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• Resumen

  • We study a non-linear Hidden Markov Model, where the process of interest is the absolute value of a discretely observed Ornstein–Uhlenbeck diffusion, which is observed after a multiplicative perturbation. We obtain explicit formulae for the recursive relations which link the relevant conditional distributions. As a consequence the predicted, filtered, and smoothed distributions for the hidden process can easily be computed. We illustrate the behaviour of these distributions on simulations.