# A Novel Theoretical Framework for Exponential Smoothing

arXiv: https://arxiv.org/abs/2403.04345 · HTML: https://mlsanity.com/paper/2403.04345/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 31 references that are in the map.
- First posted on arXiv 7 Mar 2024.

## Builds on (most cited first, 5 of 5)

- [Time-Varying Convex Optimization: Time-Structured Algorithms and Applications](https://mlsanity.com/paper/2006.08500/) (2020)
- [A Class of Prediction-Correction Methods for Time-Varying Convex Optimization](https://mlsanity.com/paper/1509.05196/) (2015)
- [Adaptive Sequential Stochastic Optimization](https://mlsanity.com/paper/1610.01970/) (2016)
- [Prediction-Correction Algorithms for Time-Varying Constrained Optimization](https://mlsanity.com/paper/1611.03681/) (2016)
- [Maximum Likelihood With a Time Varying Parameter](https://mlsanity.com/paper/2302.14529/) (2023)

## Built on by (most cited first, 1 of 1)

- [Dual Signal Decomposition of Stochastic Time Series](https://mlsanity.com/paper/2508.05915/) (2025)

## Abstract (arXiv)

Simple Exponential Smoothing is a classical technique used for smoothing time series data by assigning exponentially decreasing weights to past observations through a recursive equation; it is sometimes presented as a rule of thumb procedure. We introduce a novel theoretical perspective where the recursive equation that defines simple exponential smoothing occurs naturally as a stochastic gradient ascent scheme to optimize a sequence of Gaussian log-likelihood functions. Under this lens of analysis, our main theorem shows that -- in a general setting -- simple exponential smoothing converges to a neighborhood of the trend of a trend-stationary stochastic process. This offers a novel theoretical assurance that the exponential smoothing procedure yields reliable estimators of the underlying trend shedding light on long-standing observations in the literature regarding the robustness of simple exponential smoothing.