Peter Reinhard Hansen, Chen Tong
arXiv 15 May 2026 · Econometrics
arXiv:2605.15902 · PDF · DOI · OpenAlex · Extracted main text
Score-driven models update time-varying parameters using conditional likelihood scores. This paper develops a Bayesian interpretation of such updates through Tweedie's formula, which connects posterior mean corrections with marginal scores. In Gaussian signal extraction, this gives an exact posterior-correction identity. For natural exponential families, related identities characterize posterior means in natural- and expectation-parameter spaces. Building on these identities, we show that conjugate Bayesian filtering in expectation space coincides exactly with an inverse-Fisher-scaled conditional score update under local precision discounting. For general conditional densities, the exact Bayesian correction involves a generally unavailable predictive-marginal score. A local Gaussian approximation shows that the conditional likelihood score provides the leading approximation to this posterior correction; under local precision discounting, the predictive covariance becomes proportional to inverse Fisher information, yielding the familiar inverse-Fisher-scaled score recursion. The results clarify when score-driven updates are exact Bayesian filters and when they should instead be viewed as tractable local approximations.
appendix boundary found by none_found · 100% of the source is main text. Read the extracted text to check this.
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 | de Punder, R., Dimitriadis, T., and Lange, R.-J (2026) Expected Kullback-Leibler-based characterizations of score-driven updates | 0.928 | 4 | 3 | 100% |
| 2 | Blasques, F., Koopman, S. J., and Lucas, A (2015) Information-theoretic optimality of observation-driven time series models for continuous responses | 0.737 | 3 | 2 | 100% |
| 3 | Efron, B (2011) Tweedie's formula and selection bias | 0.737 | 3 | 2 | 100% |
| 4 | Gorgi, P., Lauria, C. S. A., and Luati, A (2024) On the optimality of score-driven models | 0.737 | 3 | 2 | 100% |
| 5 | Robbins, H (1956) An empirical Bayes approach to statistics | 0.644 | 2 | 2 | 100% |
| 6 | Tweedie, M. C. K (1984) An index which distinguishes between some important exponential families | 0.644 | 2 | 2 | 100% |
| 7 | Creal, D., Koopman, S. J., and Lucas, A (2013) Generalized autoregressive score models with applications | 0.511 | 2 | 1 | 100% |
| 8 | Harvey, A. C (2013) Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series | 0.511 | 2 | 1 | 100% |
| 9 | Masreliez, C. J (1975) Approximate non-Gaussian filtering with linear state and observation relations | 0.511 | 2 | 1 | 100% |
| 10 | West, M. and Harrison, J (1989) Bayesian Forecasting and Dynamic Models | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 28 scored citations.