基于得分驱动模型的滤波与平滑
Filtering and Smoothing with Score-Driven Models
- University of Verona（维罗纳大学）
- University of Pavia（帕维亚大学）
- University of Pisa（比萨大学）
- Scuola Normale Superiore（意大利高等师范学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文推广得分驱动模型，提出利用同期观测的更新滤波器和利用全样本的平滑器，显著降低均方误差并改善置信带覆盖，实证显示平滑估计更接近实际值。
AI中文摘要：
得分驱动模型在构造上属于纯预测性滤波器。当此类模型被解读为底层潜在过程的滤波器，而非数据生成过程时，这是一种限制而非特性，因为同期及未来的观测同样携带关于当前状态的信息。基于卡尔曼滤波器和线性高斯模型的平滑器递推可以用条件对数似然的得分来表示，且预测步骤随后呈现为得分驱动递推形式这一观察，我们沿此方向推广得分驱动模型，推导出更新滤波器和平滑器，它们分别利用同期观测和整个样本，并附带相应的条件方差。在广泛的蒙特卡洛分析中，更新滤波器将预测滤波器的均方误差降低了3.5%至8.8%，平滑器降低了32%至44%，且这一排序在每次重复中均成立；基于相关条件方差构建的置信带达到其名义覆盖率，而忽略滤波不确定性的置信带仅捕获其不到三分之一。在实证中，我们展示了将得分驱动模型用作滤波器而非纯预测过程的优势，表明所得平滑估计与已实现量的一致性高于其预测对应物。
英文摘要：
Score-driven models are, by construction, purely predictive filters. When such models are read as filters for an underlying latent process, rather than as data generating processes, this is a restriction rather than a feature, because the contemporaneous and the future observations also carry information on the current state. Starting from the observation that the Kalman filter and smoother recursions for linear Gaussian models can be written in terms of the score of the conditional log-likelihood, and that the predictive step then takes the form of a score-driven recursion, we generalize score-driven models along this direction by deriving an update filter and a smoother, which exploit the contemporaneous observation and the whole sample respectively, together with the corresponding conditional variances. In extensive Monte Carlo analyses the update filter lowers the mean square error of the predictive filter by 3.5% to 8.8%, and the smoother by 32% to 44%, with the ordering holding in every replication; confidence bands built on the associated conditional variances attain their nominal coverage, whereas bands that ignore filtering uncertainty capture less than a third of it. Empirically, we demonstrate the benefits of employing score-driven models as filters rather than as purely predictive processes, showing that the resulting smoothed estimates align more closely with realized quantities than their predictive counterparts.
