Stability and performance guarantees for misspecified multivariate score-driven filters

We consider the problem of tracking latent time-varying parameter vectors under model misspecification. We analyze implicit and explicit score-driven (ISD and ESD) filters, which update a prediction of the parameters using the gradient of the logarithmic observation density (i.e., the score). In the ESD filter, the score is computed using the predicted parameter values, whereas in the ISD filter, the score is evaluated using the new, updated parameter values. For both filter types, we derive novel sufficient conditions for the exponential stability (i.e., invertibility) of the filtered parameter path and existence of a finite mean squared error (MSE) bound with respect to the pseudo-true parameter path. In addition, we present expressions for finite-sample and asymptotic MSE bounds. Our performance guarantees rely on mild moment conditions on the data-generating process, while our stability result is entirely agnostic about the true process. As a result, our primary conditions depend only on the characteristics of the filter; hence, they are verifiable in practice. Concavity of the postulated log density combined with simple parameter restrictions is sufficient (but not necessary) for ISD-filter stability, whereas ESD-filter stability additionally requires the score to be Lipschitz continuous. Extensive simulation studies validate our theoretical findings and demonstrate the enhanced stability and improved performance of ISD over ESD filters. An empirical application to U.S. Treasury-bill rates confirms the practical relevance of our contribution.