Rutger-Jan Lange, Bram van Os, Dick van Dijk
arXiv 2 Dec 2025 · Statistics — Methodology · publishedJournal of Econometrics (2026)
arXiv:2512.02744 · PDF · DOI · OpenAlex · Extracted main text
We propose an observation-driven modeling framework that permits time variation in the model parameters using 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 if the observation log density is linearly approximated around the prediction. By preserving the full density, the ISD update globalizes favorable local properties of the ESD update. Namely, for log-concave observation densities, whether correctly specified or not, the ISD filter is stable for all learning rates, while 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 illustrations in finance and macroeconomics.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Asi, H. and J. C. Duchi (2019) Stochastic (approximate) proximal point methods: Convergence, optimality, and adaptivity | 1.000 | 8 | 3 | 100% |
| 2 | Creal, D., S. J. Koopman, and A. Lucas (2013) Generalized autoregressive score models with applications | 1.000 | 7 | 4 | 100% |
| 3 | Lange, R.-J (2024) Bellman filtering and smoothing for state–space models self | 1.000 | 5 | 3 | 100% |
| 4 | Koopman, S. J., A. Lucas, and M. Scharth (2016) Predicting time-varying parameters with parameter-driven and observation-driven models | 0.950 | 7 | 4 | 86% |
| 5 | Artemova, M., F. Blasques, J. van Brummelen, and S. J. Koopman (2022) Score-driven models: Methodology and theory | 0.941 | 6 | 4 | 83% |
| 6 | Harvey, A. C (2013) Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series | 0.928 | 4 | 3 | 100% |
| 7 | Rockafellar, R. T (1976) Monotone operators and the proximal point algorithm | 0.874 | 5 | 2 | 100% |
| 8 | Boyd, S. and L. Vandenberghe (2004) Convex Optimization | 0.843 | 3 | 3 | 100% |
| 9 | Nesterov, Y (2018) Lectures on Convex Optimization | 0.843 | 3 | 3 | 100% |
| 10 | Straumann, D. and T. Mikosch (2006) Quasi-maximum-likelihood estimation in conditionally heteroscedastic time series: A stochastic recurrence equations approach | 0.843 | 3 | 3 | 100% |
Showing the top 10 of 82 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Expected Kullback-Leibler-based characterizations of score-driven updates | 0.737 | 5 | 3 |
| 2 | Exponentially weighted estimands and the exponential family: Filtering, prediction and smoothing | 0.511 | 3 | 2 |
| 3 | Tweedie’s Formula and Score-Driven Updating | 0.405 | 1 | 1 |