Published in:Banque de France Working Paper ; No. 486
Extent:
1 Online-Ressource (52 p)
Language:
English
DOI:
10.2139/ssrn.2450089
Identifier:
Origination:
Footnote:
Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments June 2014 erstellt
Description:
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