We propose using a discounted version of a convex combination of the log-likelihood with the corresponding expected log-likelihood such that when they are maximized they yield a filter, predictor and smoother for time series. This paper then focuses on working out the implications of this in the case of the canonical exponential family. The results are simple exact filters, predictors and smoothers with linear recursions. A theory for these models is developed and the models are illustrated on simulated and real data.

翻译：我们提出使用对数似然函数与相应期望对数似然函数的凸组合的折现版本，通过最大化该组合得到时间序列的滤波、预测和平滑方法。本文随后重点推导了该框架在标准指数族情况下的具体实现。所得结果为具有线性递推形式的简单精确滤波、预测与平滑器。本文发展了这类模型的理论体系，并通过模拟数据与真实数据进行了模型展示。