We propose an observation-driven modeling framework that allows model parameters to vary over time through 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 when the observation log density is linearly approximated around the prediction. By preserving the full density, the ISD update extends the favorable local properties of the ESD update to a global setting. For log-concave observation densities, whether correctly specified or not, the ISD filter is stable for all learning rates, and 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 applications in finance and macroeconomics.

翻译：我们提出一种观测驱动建模框架，该框架通过隐式得分驱动更新实现模型参数随时间动态变化。ISD更新在惩罚相对于一步前预测参数加权L2范数的同时，最大化参数向量的对数观测密度，从而生成隐式随机梯度更新。研究表明，当观测对数密度在预测值附近进行线性近似时，便得到流行的显式得分驱动模型类别。通过保留完整密度函数，ISD更新将ESD更新优良的局部性质扩展至全局场景。对于对数凹观测密度（无论模型设定正确与否），ISD滤波器在所有学习率下均保持稳定，其更新在均方误差意义上向每时刻(伪)真实参数呈收缩特性。我们通过金融与宏观经济学领域的模拟及实证应用验证了ISD滤波器的有效性。