Filtering and Smoothing with Score-Driven Models
33 Pages Posted: 14 Mar 2018 Last revised: 2 Dec 2019
Date Written: November 29, 2019
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: Suggested Citation