A0269
Title: Stability and performance guarantees for misspecified multivariate score-driven filters
Authors: Rutger-Jan Lange - Econometric Institute (Netherlands) [presenting]
Simon Donker van Heel - Econometric Institute Erasmus University Rotterdam (Netherlands)
Bram van Os - School of Business and Economics Vrije Universiteit Amsterdam (Netherlands)
Dick van Dijk - Econometric Institute Erasmus University Rotterdam (Netherlands)
Abstract: The problem of tracking latent time-varying parameter vectors under model misspecification is considered. Implicit and explicit score-driven (ISD and ESD) filters are analyzed, 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, novel sufficient conditions are derived for the exponential stability (i.e., invertibility) of the filtered parameter path and the existence of a finite mean squared error (MSE) bound with respect to the pseudo-true parameter path. In addition, expressions for finite-sample and asymptotic MSE bounds are presented. The performance guarantees rely on mild moment conditions in the data-generating process, while the stability result is entirely agnostic about the true process. The 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 the 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 the contribution.
