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A Quadratic Kalman Filter

Listed author(s):
  • Monfort, A.
  • Renne, J.-P.
  • Roussellet, G.

We propose a new filtering and smoothing technique for non-linear state-space models. Observed variables are quadratic functions of latent factors following a Gaussian VAR. Stacking the vector of factors with its vectorized outer-product, we form an augmented state vector whose first two conditional moments are known in closed-form. We also provide analytical formulae for the unconditional moments of this augmented vector. Our new quadratic Kalman filter (Qkf) exploits these properties to formulate fast and simple filtering and smoothing algorithms. A first simulation study emphasizes that the Qkf outperforms the extended and unscented approaches in the filtering exercise showing up to 70% RMSEs improvement of filtered values. Second, we provide evidence that Qkf-based maximum-likelihood estimates of model parameters always possess lower bias or lower RMSEs that the alternative estimators.

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File URL: https://publications.banque-france.fr/sites/default/files/medias/documents/working-paper_486_2014.pdf
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Paper provided by Banque de France in its series Working papers with number 486.

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Length: 52 pages
Date of creation: 2014
Handle: RePEc:bfr:banfra:486
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Banque de France 31 Rue Croix des Petits Champs LABOLOG - 49-1404 75049 PARIS

Web page: http://www.banque-france.fr/

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