A Quadratic Kalman Filter

Details

Serval ID
serval:BIB_D3636358D4E9
Type
Article: article from journal or magazin.
Collection
Publications
Title
A Quadratic Kalman Filter
Journal
Journal of Econometrics
Author(s)
Monfort A., Renne J.-P., Roussellet G.
ISSN
0304-4076
Publication state
Published
Issued date
2015
Peer-reviewed
Oui
Volume
187
Number
1
Pages
43-56
Language
english
Notes
Monfort_Renne_Roussellet_2015
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
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Create date
23/09/2015 15:46
Last modification date
20/08/2019 15:53
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