Filtering and Smoothing with Score-Driven Models

39 Pages Posted: 14 Mar 2018 Last revised: 22 Feb 2021

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: February 20, 2021

Abstract

We propose a methodology for filtering, smoothing and assessing parameter and filtering uncertainty in score-driven models. Our technique is based on a general representation of the Kalman filter and smoother recursions for linear Gaussian models in terms of the score of the conditional log-likelihood. We prove that, when data is generated by a nonlinear non-Gaussian state-space model, the proposed methodology results from a local expansion of the true filtering density. A formal characterization of the approximation error is provided. 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 approximate filters rather than purely predictive processes.

Keywords: State-Space models, Score-driven models, Kalman filter, Smoothing, 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 (February 20, 2021). 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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