Simon Donker van Heel, Neil Shephard
arXiv 18 Dec 2025 · Statistics — Methodology
arXiv:2512.16745 · PDF · Extracted main text
We propose using a discounted version of a convex combination of the log-likelihood with the corresponding expected log-likelihood such that when they are maximized they yield a filter, predictor and smoother for time series. This paper then focuses on working out the implications of this in the case of the canonical exponential family. The results are simple exact filters, predictors and smoothers with linear recursions. A theory for these models is developed and the models are illustrated on simulated and real data.
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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 | |
|---|---|---|---|---|---|
| Harvey(13) | unmatched citation key Harvey(13) | 0.843 | 4 | 3 | 75% |
| CrealKoopmanLucas(13) | unmatched citation key CrealKoopmanLucas(13) | 0.843 | 5 | 3 | 60% |
| McCullaghNelder(89) | unmatched citation key McCullaghNelder(89) | 0.843 | 3 | 3 | 100% |
| BenjaminRigbyStasinopoulos(03) | unmatched citation key BenjaminRigbyStasinopoulos(03) | 0.737 | 3 | 2 | 100% |
| 5 | Lange, Rutger-Jan and van Os, Bram and van Dijk, Dick JC (2024) Implicit score-driven filters for time-varying parameter models | 0.511 | 3 | 2 | 33% |
| Cox(61) | unmatched citation key Cox(61) | 0.511 | 2 | 1 | 100% |
| DurbinKoopman(12) | unmatched citation key DurbinKoopman(12) | 0.511 | 2 | 1 | 100% |
| Huber(67) | unmatched citation key Huber(67) | 0.511 | 2 | 1 | 100% |
| AbramowitzStegun(70) | unmatched citation key AbramowitzStegun(70) | 0.405 | 1 | 1 | 100% |
| Bollerslev(86) | unmatched citation key Bollerslev(86) | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 45 scored citations. 9 of these could not be matched to a bibliography entry, so only the citation key is shown.