A Quadratic Kalman Filter

39 Pages Posted: 21 Dec 2013 Last revised: 25 Nov 2014

See all articles by Alain Monfort

Alain Monfort

National Institute of Statistics and Economic Studies (INSEE) - Center for Research in Economics and Statistics (CREST); National Bureau of Economic Research (NBER); Maastricht University

Jean-Paul Renne

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne)

Guillaume Roussellet

McGill University - Desautels Faculty of Management

Multiple version iconThere are 2 versions of this paper

Date Written: November 1, 2014

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

JEL Classification: C32, C46, C53, C57

Suggested Citation

Monfort, Alain and Renne, Jean-Paul and Roussellet, Guillaume, A Quadratic Kalman Filter (November 1, 2014). Available at SSRN: https://ssrn.com/abstract=2369788 or http://dx.doi.org/10.2139/ssrn.2369788

Alain Monfort

National Institute of Statistics and Economic Studies (INSEE) - Center for Research in Economics and Statistics (CREST) ( email )

15 Boulevard Gabriel Peri
Malakoff Cedex, 1 92245
France
+33 1 4117 6079 (Phone)
+33 1 4117 6046 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Maastricht University

P.O. Box 616
Maastricht, 6200MD
Netherlands

Jean-Paul Renne

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne) ( email )

Unil Dorigny, Batiment Internef
Lausanne, 1015
Switzerland

Guillaume Roussellet (Contact Author)

McGill University - Desautels Faculty of Management ( email )

1001 Sherbrooke St. West
Montreal, Quebec H3A1G5 H3A 2M1
Canada

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