发表机构
Scuola Normale Superiore; The London School of Economics and Political Science（高等师范学院; 伦敦政治经济学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对得分驱动滤波器的增益这一决策变量，提出基于 Kullback-Leibler 目标的在线学习方法，通过镜像下降更新建立动态遗憾界，在股指波动率预测中验证其优于恒定增益且能避免极端峰值。
AI 中文摘要
得分驱动滤波器将缩放后的对数似然得分乘以一个控制更新幅度的增益，我们将该增益视为决策变量并研究其在线学习。在当前状态、观测值、得分和缩放规则的条件下，每个可行增益会诱导出一个可达的下一状态和一步 ahead 预测密度：标量增益控制沿直线的距离，对角增益则控制逐坐标的传输。因此，增益选择是一个以 Kullback-Leibler 为目标的条件预测决策问题。对于标量未缩放增益，连续得分的负原始乘积是该损失的随机梯度；正 aGAS 缩放仅重新调整有效步长。单调可微增益链接在有界增益域上诱导镜像下降几何，而持续性则产生指向参考增益的 Bregman 拉力。在凸性、紧性和正则性条件下，我们针对投影和折扣镜像更新，相对于时变、当前信息比较器建立了动态遗憾界。模拟说明了缩放、链接几何、持续性和逐坐标传输率的作用。股指波动率的样本外面板显示，有界镜像增益通常匹配或优于恒定增益，同时避免了名义上无界指数链接的极端峰值，在多危机市场中观察到最强的改进。
英文摘要
A score-driven filter multiplies its scaled log-likelihood score by a scale parameter. We call this coefficient the gain and learn it online. Given the current state and realised scaled score, each admissible gain selects a reachable next state and predictive density. A scalar gain moves along a line; diagonal gains control coordinatewise transmission and may change direction. We evaluate gain selection using a one-step predictive Kullback-Leibler objective. In the scalar unscaled case, the negative consecutive-score product is a stochastic gradient; the positive product used in accelerated recursions is a descent direction. Positive scalar score scaling changes only the effective learning rate. Strictly increasing, continuously differentiable gain links with positive derivative induce mirror-descent geometry, while persistence adds a Bregman pull towards a reference gain. Under convexity, compactness, integrability, and schedule conditions, projected and discounted mirror updates satisfy dynamic-regret bounds relative to time-varying, current-information comparators. Simulations isolate score scaling, link geometry, persistence, and coordinatewise gains. Across twelve equity indices, the bounded discounted-logistic gain records a lower out-of-sample mean negative log score than the constant gain in eleven markets, although market-level evidence is mixed. It also avoids the extreme transients of the numerically capped exponential-link benchmark.
Comments63 pages, 10 figures, 13 tables
