Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2022-09-20
Revision-Date: 2024-11-21
Number: 22-066/III
Author-Name: Rutger-Jan Lange
Author-Workplace-Name: Erasmus University Rotterdam 
Author-Name: Bram van Os
Author-Workplace-Name: Erasmus University Rotterdam 
Author-Name: Dick van Dijk
Author-Workplace-Name: Erasmus University Rotterdam
Title: Implicit score-driven filters for time-varying parameter models
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.
Classification-JEL: C10, C32, C51
Keywords: Implicit gradient, Proximal-point method, Stochastic-gradient descent, Observation-driven models
File-URL: https://papers.tinbergen.nl/22066.pdf
File-Format: application/pdf
File-Size: 1.203.249 bytes
Handle: RePEc:tin:wpaper:20220066