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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2605.15902 |
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| _version_ | 1866918524525477888 |
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| author | Hansen, Peter Reinhard Tong, Chen |
| author_facet | Hansen, Peter Reinhard Tong, Chen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15902 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tweedie's Formula and Score-Driven Updating Hansen, Peter Reinhard Tong, Chen Econometrics Methodology 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. |
| title | Tweedie's Formula and Score-Driven Updating |
| topic | Econometrics Methodology |
| url | https://arxiv.org/abs/2605.15902 |