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：我们提出采用对数似然函数与其期望对数似然函数凸组合的折扣形式，通过最大化该组合可得到时间序列的滤波器、预测器和平滑器。本文重点探讨这一方法在典型指数族情形下的理论内涵。研究结果得到了具有线性递推关系的简洁精确滤波器、预测器和平滑器。本文建立了相关模型的理论框架，并通过模拟数据与真实数据进行了模型验证。