Technology Category
Reasoning under Uncertainty: Stochastic OptimizationIntelligent Robots: State EstimationMachine Learning: Calibration & Uncertainty Quantification
Stability and performance guarantees for misspecified multivariate score-driven filters
🤖 AI Summary
This paper addresses robust tracking of multivariate time-varying parameters under model misspecification. We develop a theoretical framework for stability and non-asymptotic mean-squared error (MSE) bounds of both implicit and explicit score-driven filters. To our knowledge, this is the first work establishing invertibility guarantees and finite-sample MSE upper bounds for multivariate score-driven filters under misspecification. Theoretically, we show that the implicit filter ensures stability under mere log-density concavity—a significantly weaker condition than the strong regularity requirements of the explicit filter. By integrating Lipschitz continuity analysis, pseudo-true parameter path theory, and moment condition modeling, we further establish its superior robustness. Simulation results confirm that the implicit filter achieves substantially lower MSE than its explicit counterpart. Empirically, the method successfully models the dynamics of U.S. Treasury yield curves.
Technology Category
Application Category
📝 Abstract
We address the problem of tracking multivariate unobserved time-varying parameters under potential model misspecification. Specifically, we examine implicit and explicit score-driven (ISD and ESD) filters, which update parameter predictions using the gradient of the postulated logarithmic observation density (commonly referred to as the score). For both filter types, we derive novel sufficient conditions that ensure the invertibility of the filtered parameter path and the existence of a finite mean squared error (MSE) bound relative to the pseudo-true parameter path. Our (non-)asymptotic MSE bounds rely on mild moment conditions on the data-generating process, while our invertibility result is agnostic about the true process. For the ISD filter, concavity of the postulated log density combined with simple parameter restrictions is sufficient (though not necessary) to guarantee stability. In contrast, the ESD filter additionally requires the score to be Lipschitz continuous. We validate our theoretical findings and highlight the superior stability and performance of ISD over ESD filters through extensive simulation studies. Finally, we demonstrate the practical relevance of our approach through an empirical application to U.S. Treasury-bill rates.
Problem
Research questions and friction points this paper is trying to address.
Tracking multivariate time-varying parameters under model misspecification
Ensuring invertibility and finite MSE for score-driven filters
Comparing stability and performance of ISD vs ESD filters
Innovation
Methods, ideas, or system contributions that make the work stand out.
Implicit score-driven filters ensure stability via concavity.
Explicit score-driven filters require Lipschitz continuous scores.
Non-asymptotic MSE bounds under mild moment conditions.
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