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A Quadratic Kalman Filter

Alain Monfort (), Jean-Paul Renne and Guillaume Roussellet ()

Journal of Econometrics, 2015, vol. 187, issue 1, 43-56

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 simulation study first emphasizes that the Qkf outperforms the extended and unscented approaches in the filtering exercise showing up to 70% RMSEs improvement of filtered values. Second, it provides evidence that Qkf-based maximum-likelihood estimates of model parameters always possess lower bias or lower RMSEs than the alternative estimators.

Keywords: Non-linear filtering; Non-linear smoothing; Quadratic model; Kalman filter; Quasi maximum likelihood (search for similar items in EconPapers)
JEL-codes: C32 C46 C53 (search for similar items in EconPapers)
Date: 2015
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Working Paper: A Quadratic Kalman Filter (2014) Downloads
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:187:y:2015:i:1:p:43-56

DOI: 10.1016/j.jeconom.2015.01.003

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