Exponentially weighted estimands and the exponential family: filtering, prediction and smoothing

Simon Donker van Heel and Neil Shephard
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Simon Donker van Heel: Erasmus University Rotterdam
Neil Shephard: Harvard University

No 25-074/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

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.

Keywords: Exponential family; EWMA; Filtering; Likelihood; Time Series (search for similar items in EconPapers)
JEL-codes: C1 C32 (search for similar items in EconPapers)
Date: 2025-12-18, Revised 2026-05-05
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