Ramon de Punder, Timo Dimitriadis, Rutger-Jan Lange
arXiv 5 Aug 2024 · Mathematics — Statistics Theory · 1 citations (OpenAlex)
arXiv:2408.02391 · PDF · DOI · OpenAlex · Extracted main text
Score-driven models have been applied in some 400 published articles over the last decade. Much of this literature cites the optimality result in Blasques et al. (2015), which, roughly, states that sufficiently small score-driven updates are unique in locally reducing the Kullback-Leibler divergence relative to the true density for every observation. This is at odds with other well-known optimality results; the Kalman filter, for example, is optimal in a mean-squared-error sense, but occasionally moves away from the true state. We show that score-driven updates are, similarly, not guaranteed to improve the localized Kullback-Leibler divergence at every observation. The seemingly stronger result in Blasques et al. (2015) is due to their use of an improper (localized) scoring rule. Even as a guaranteed improvement for every observation is unattainable, we prove that sufficiently small score-driven updates are unique in reducing the Kullback-Leibler divergence relative to the true density in expectation. This positive, albeit weaker, result justifies the continued use of score-driven models and places their information-theoretic properties on solid footing.
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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 | Creal, D., S. J. Koopman, A. Lucas, and M. Zamojski (2024) Observation-driven filtering of time-varying parameters using moment conditions | 0.956 | 24 | 6 | 88% |
| 2 | Gorgi, P., C. S. Lauria, and A. Luati (2024) On the optimality of score-driven models | 0.955 | 31 | 7 | 87% |
| 3 | Creal, D., S. J. Koopman, and A. Lucas (2013) Generalized autoregressive score models with applications | 0.874 | 5 | 2 | 100% |
| 4 | Gasperoni, F., A. Luati, L. Paci, and E. D’Innocenzo (2023) Score-driven modeling of spatio-temporal data | 0.811 | 4 | 2 | 100% |
| 5 | Blasques, F., S. J. Koopman, and A. Lucas (2015) Information-theoretic optimality of observation-driven time series models for continuous responses | 0.774 | 28 | 6 | 46% |
| 6 | Diks, C., V. Panchenko, and D. J. van Dijk (2011) Likelihood-based scoring rules for comparing density forecasts in tails | 0.737 | 5 | 3 | 40% |
| 7 | Lange, R.-J., B. van Os, and D. J. van Dijk (2025) Implicit score-driven filters for time-varying parameter models self | 0.737 | 5 | 3 | 40% |
| 8 | Gneiting, T. and R. Ranjan (2011) Comparing density forecasts using threshold- and quantile-weighted scoring rules | 0.737 | 3 | 3 | 67% |
| 9 | D’Innocenzo, E., A. Lucas, B. Schwaab, and X. Zhang (2024) Modeling extreme events: Time-varying extreme tail shape | 0.737 | 3 | 2 | 100% |
| 10 | Harvey, A. C. and A. Luati (2014) Filtering with heavy tails | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 37 scored citations.