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 permits time variation in the model’s parameters using an implicit score-driven (ISD) update. The ISD update maximizes the observation log density with respect to the parameter vector, while penalizing the weighted l2 norm relative to the one-step-ahead prediction. This yields an implicit stochastic-gradient update; taking instead the explicit version produces the popular class of explicit score-driven (ESD) models. Specifically, we show that the ESD update arises as a linearization of the ISD update. By preserving the full density, the ISD update globalizes favorable local properties of the ESD update. Namely, for log-concave observation densities (even when misspecified), ISD models are stable for any learning rate and globally contractive to a pseudo-truth. We demonstrate the usefulness of ISD models in simulations and empirical illustrations for 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 2024-11-21
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (2)

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