Beyond the normal approximation: robust filtering and smoothing via perturbation methods

45 Pages Posted: 14 Mar 2018 Last revised: 31 May 2023

See all articles by Giuseppe Buccheri

Giuseppe Buccheri

University of Verona - Department of Economics

Giacomo Bormetti

University of Pavia - Department of Economics and Management

Fulvio Corsi

University of Pisa - Department of Economics

Fabrizio Lillo

Università di Bologna

Date Written: May 29, 2023

Abstract

Using a perturbation technique, we derive a new approximate filtering and smoothing methodology generalizing along different directions several existing approaches to robust filtering based on the score and the Hessian matrix of the observation density. The main advantages of the methodology can be summarized as follows: (i) it relaxes the critical assumption of a Gaussian conditional distribution for the latent states underlying such approaches; (ii) can be applied to a general class of state-space models including location, scale and count data models; (iii) rationalizes the approximation to the likelihood function within the same perturbation approach, thus allowing for straightforward inference of the model parameters; (iv) enables the computation of confidence bands around the state estimates reflecting the combination of parameter and filtering uncertainty. We show through an extensive Monte Carlo study that the mean square loss with respect to exact simulation-based methods is small in a wide range of scenarios. We finally illustrate empirically the application of the methodology to the estimation of stochastic volatility and correlations in financial time-series.

Keywords: Nonlinear filtering, time-varying parameters, stochastic volatility, dynamic correlations

JEL Classification: C22, C32, C58

Suggested Citation

Buccheri, Giuseppe and Bormetti, Giacomo and Corsi, Fulvio and Lillo, Fabrizio, Beyond the normal approximation: robust filtering and smoothing via perturbation methods (May 29, 2023). Available at SSRN: https://ssrn.com/abstract=3139666 or http://dx.doi.org/10.2139/ssrn.3139666

Giuseppe Buccheri (Contact Author)

University of Verona - Department of Economics ( email )

Via Cantarane, 24
37129 Verona
Italy
045 8028525 (Phone)

Giacomo Bormetti

University of Pavia - Department of Economics and Management

Via San Felice al Monastero 5
Pavia, 27100
Italy

Fulvio Corsi

University of Pisa - Department of Economics ( email )

via Ridolfi 10
I-56100 Pisa, PI 56100
Italy

HOME PAGE: http://people.unipi.it/fulvio_corsi/

Fabrizio Lillo

Università di Bologna ( email )

Via Zamboni, 33
Bologna, 40126
Italy

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