Filtering and Smoothing with Score-Driven Models

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.