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

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  • Simon Donker van Heel
  • Neil Shephard

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.

Suggested Citation

  • Simon Donker van Heel & Neil Shephard, 2025. "Exponentially weighted estimands and the exponential family: filtering, prediction and smoothing," Papers 2512.16745, arXiv.org, revised Jan 2026.
    • Handle: RePEc:arx:papers:2512.16745
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    References listed on IDEAS

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    6. Eric Luxenberg & Stephen Boyd, 2024. "Exponentially Weighted Moving Models," Papers 2404.08136, arXiv.org, revised Apr 2024.
    7. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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