Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/339077 
Year of Publication: 
2026
Series/Report no.: 
Tinbergen Institute Discussion Paper No. TI 2025-074/III
Version Description: 
Revision: January 2026
Publisher: 
Tinbergen Institute, Amsterdam and Rotterdam
Abstract: 
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.
Subjects: 
Exponential family
EWMA
Filtering
Likelihood
Time Series
JEL: 
C1
C32
Document Type: 
Working Paper

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