Tweedie's Formula and Score-Driven Updating

Peter Hansen and Chen Tong

Papers from arXiv.org

Abstract: Tweedie's formula expresses a conditional mean in terms of a score function, and this connects score-driven models with Bayesian updating. We show that the score-driven update is identical to a Bayesian update in some special cases. More generally, we show that score-driven updating is a local approximation to Bayesian updating, with an error of second order in the predictive variance. The second-order approximation error has two components, one from the curvature of the log likelihood and one from the asymmetry of the posterior distribution. Implicit score-driven (ISD) updating, which evaluates the score at the updated parameter, corrects for the former but not the latter. A simple correction for the second component leads to an improved third-order approximation, which we denote ISD*. Numerical experiments show substantial gains from ISD and ISD*.

Date: 2026-05, Revised 2026-10
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-mac
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