Robust Filtering

48 Pages Posted: 4 Aug 2012

See all articles by Laurent E. Calvet

Laurent E. Calvet

SKEMA Business School; CEPR

Veronika Czellar

SKEMA Business School

Elvezio Ronchetti

University of Geneva - Research Center for Statistics

Date Written: June 25, 2012


Filtering methods are powerful tools to estimate the hidden state of a state-space model from observations available in real time. However, they are known to be highly sensitive to the presence of small misspecifications of the underlying model and to outliers in the observation process. In this paper, we show that the methodology of robust statistics can be adapted to the framework of sequential filtering. We introduce an impact function that quantifies the sensitivity of the state distribution with respect to new data. Since the impact function of a standard filter is unbounded even in the simplest cases, we propose a filter with a bounded impact function which provides accurate state and parameter inference in the presence of model misspecifications. We illustrate its good properties in several examples including linear models and nonlinear financial models of stochastic volatility.

Keywords: Kalman filter, particle filter, robust statistics, state space model, stochastic volatility

JEL Classification: C11, C13, C15, C22

Suggested Citation

Calvet, Laurent E. and Czellar, Veronika and Ronchetti, Elvezio, Robust Filtering (June 25, 2012). Available at SSRN: or

Laurent E. Calvet (Contact Author)

SKEMA Business School ( email )

5 Quai Marcel Dassault
Suresnes, 92150

CEPR ( email )

33 Great Sutton Street
London, EC1V 0DX
United Kingdom

Veronika Czellar

SKEMA Business School ( email )

5 quai Marcel Dassault
Suresnes, 92156

Elvezio Ronchetti

University of Geneva - Research Center for Statistics ( email )

Blv. Pont d'Arve 40
1211 Geneva 4


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