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.