We propose an observation-driven modeling framework that permits time variation in the model parameters using an implicit score-driven (ISD) update. The ISD update maximizes the logarithmic observation density with respect to the parameter vector, while penalizing the weighted L2 norm relative to a one-step-ahead predicted parameter. This yields an implicit stochastic-gradient update. We show that the popular class of explicit score-driven (ESD) models arises if the observation log density is linearly approximated around the prediction. By preserving the full density, the ISD update globalizes favorable local properties of the ESD update. Namely, for log-concave observation densities, whether correctly specified or not, the ISD filter is stable for all learning rates, while its updates are contractive in mean squared error toward the (pseudo-)true parameter at every time step. We demonstrate the usefulness of ISD filters in simulations and empirical illustrations in finance and macroeconomics.

翻译：我们提出了一种观测驱动建模框架，通过隐式得分驱动更新机制实现模型参数的时变性。ISD更新在最大化参数向量对数观测密度的同时，对相对于一步超前预测参数的加权L2范数进行惩罚，从而形成隐式随机梯度更新。研究表明，若在预测点处对观测对数密度进行线性近似，即可导出广泛应用的显式得分驱动模型类别。通过保持完整密度形式，ISD更新将ESD更新的优良局部性质全局化。具体而言，对于对数凹观测密度（无论设定正确与否），ISD滤波器在所有学习率下均保持稳定，且其更新在均方误差意义下以压缩映射方式收敛于每时刻的（伪）真实参数。我们通过金融与宏观经济领域的仿真模拟与实证案例，验证了ISD滤波器的实用价值。