恰当评分观测驱动滤波器：局部几何、估计与连续时间极限
Proper-score observation-driven filters: local geometry, estimation, and continuous-time limits
- London School of Economics and Political Science（伦敦政治经济学院）
- Scuola Normale Superiore（比萨高等师范学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究提出基于恰当评分规则的观测驱动滤波器，推导其局部动力学、渐近性质与连续时间极限，通过实验验证其在金融收益数据中的应用，为误设下的观测驱动滤波提供准则框架。
AI中文摘要：
观测驱动滤波器通过似然评分更新时变参数，将递归与对数评分规则关联。我们在给定的工作族和可预测缩放范围内，用可微恰当评分规则的负参数导数替代该更新。对于一般规则，条件均值更新是条件评分风险的预条件随机梯度；当包含自回归牵引时，中心为复合均值场的零点。我们推导了局部实现损失下降和条件均值收缩结果，并将局部动力学分解为风险曲率和创新变异性。根据Bartlett恒等式，这两个量在对数评分下一致，但通常不同，这阐明了有界驱动如何限制极端观测向滤波路径的传递。我们还为静态递归参数的批最小评分风险估计建立了一致性和相依数据三明治渐近正态性。对于高频尺度模型，中心化更新产生扩散极限，非中心化更新产生均值流极限，局部转移定理给出了围绕移动评分规则风险投影的Ornstein-Uhlenbeck近似。工作族、评分规则、缩放和自回归参数共同决定滤波路径，而工作族还决定预测分位数。受控实验说明了这些通道。针对国际股票收益的按准则的经验密度析因，在不施加通用排名的情况下评估了点方差损失、风险价值覆盖和概率积分变换诊断。结果为误设下的观测驱动滤波提供了基于准则的框架，并确定了估计、局部跟踪和连续时间近似所需的假设。
英文摘要：
Observation-driven filters typically use likelihood-score updates, corresponding to the logarithmic scoring rule. We generalise these updates to negative parameter derivatives of differentiable proper scoring rules, under a declared working family and predictable scaling. The rule determines the conditional risk projection and tail response, scaling converts its derivative into the update, and the autoregressive component determines the composite dynamic centre. Locally, risk curvature and scaling govern mean reversion, while the variance of the scaled innovation governs update noise. Under correct specification, unscaled curvature and score variance coincide for the log score by the information identity, but generally differ for other proper rules. For static parameters, we establish consistency and asymptotic normality under explicit stability and fixed-tuning conditions. In high-frequency scale models, centred updates converge to diffusions, whereas non-centred updates follow deterministic mean flows. For time-varying rule-specific projections, the local tracking error admits an Ornstein-Uhlenbeck approximation up to a stopping time, allowing correlated update and target shocks. Simulations and an international-equity application illustrate how criterion choice affects robustness, adaptation, variance-forecast loss, value-at-risk calibration and probability-integral-transform diagnostics. Predictive density and updating criterion are distinct design choices whose relative performance depends on the target and disturbance.
