A Quadratic Kalman Filter

Alain Monfort, Jean-Paul Renne and Guillaume Roussellet

Working papers from Banque de France

Abstract: 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.

Keywords: non-linear filtering; non-linear smoothing; quadratic model; Kalman filter; pseudo-maximum likelihood. (search for similar items in EconPapers)
JEL-codes: C32 C46 C53 C57 (search for similar items in EconPapers)
Pages: 52 pages
Date: 2014
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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Journal Article: A Quadratic Kalman Filter (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:bfr:banfra:486

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