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的建模框架，该框架通过隐式得分驱动更新实现模型参数的时变性。ISD更新相对于参数向量最大化对数观测密度，同时惩罚相对于一步超前预测参数的加权L2范数，从而产生隐式随机梯度更新。我们证明，若在预测点附近对观测对数密度进行线性近似，则可导出流行的显式得分驱动模型类。通过保留完整密度，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与实证案例，展示了ISD滤波器的实用价值。