Implicit score-driven filters for time-varying parameter models

Rutger-Jan Lange, Bram van Os and Dick van Dijk
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Bram van Os: Erasmus University Rotterdam

No 22-066/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: We propose an observation-driven modeling framework that allows model parameters to vary over time through an implicit score-driven (ISD) update. The ISD update maximizes the logarithmic observation density with respect to the parameter vector while penalizing the weighted L2 norm relative to a one-step-ahead predicted parameter. This yields an implicit stochastic-gradient update. We show that the popular class of explicit score-driven (ESD) models arises when the observation log density is linearly approximated around the prediction. By preserving the full density, the ISD update extends the favorable local properties of the ESD update to a global setting. For log-concave observation densities, whether correctly specified or not, the ISD filter is stable for all learning rates, and its updates are contractive in mean squared error toward the (pseudo-)true parameter at every time step. We demonstrate the usefulness of ISD filters in simulations and empirical applications in finance and macroeconomics.

Keywords: Implicit gradient; Proximal-point method; Stochastic-gradient descent; Observation-driven models (search for similar items in EconPapers)
JEL-codes: C10 C32 C51 (search for similar items in EconPapers)
Date: 2022-09-20, Revised 2026-04-23
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (3)

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Working Paper: Implicit score-driven filters for time-varying parameter models (2026)
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