Filtering and Smoothing with Score-Driven Models

33 Pages Posted: 14 Mar 2018 Last revised: 2 Dec 2019

See all articles by Giuseppe Buccheri

Giuseppe Buccheri

University of Rome Tor Vergata

Giacomo Bormetti

University of Bologna - Department of Mathematics

Fulvio Corsi

University of Pisa - Department of Economics; City University London

Fabrizio Lillo

Università di Bologna

Date Written: November 29, 2019

Abstract

We propose a methodology for filtering, smoothing and assessing parameter and filtering uncertainty in misspecified score-driven models. Our technique is based on a general representation of the well-known Kalman filter and smoother recursions for linear Gaussian models in terms of the score of the conditional log-likelihood. We prove that, when data are generated by a nonlinear non-Gaussian state-space model, the proposed methodology results from a first-order expansion of the true observation density around the optimal filter. The error made by such approximation is assessed analytically. As shown in extensive Monte Carlo analyses, our methodology performs very similarly to exact simulation-based methods, while remaining computationally extremely simple. We illustrate empirically the advantages in employing score-driven models as misspecified filters rather than purely predictive processes.

Keywords: Score-driven models, Smoothing, Kalman filter, State-Space models, Filtering uncertainty

JEL Classification: C22, C32, C58

Suggested Citation

Buccheri, Giuseppe and Bormetti, Giacomo and Corsi, Fulvio and Lillo, Fabrizio, Filtering and Smoothing with Score-Driven Models (November 29, 2019). Available at SSRN: https://ssrn.com/abstract=3139666 or http://dx.doi.org/10.2139/ssrn.3139666

Giuseppe Buccheri (Contact Author)

University of Rome Tor Vergata ( email )

Via columbia 2
Rome, Rome 00123
Italy
39 06 72595945 (Phone)

Giacomo Bormetti

University of Bologna - Department of Mathematics ( email )

Piazza di Porta S. Donato , 5
Bologna, Bologna 40126
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/

City University London ( email )

Northampton Square
London, EC1V OHB
United Kingdom

Fabrizio Lillo

Università di Bologna ( email )

Via Zamboni, 33
Bologna, 40126
Italy

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