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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.04345 |
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| _version_ | 1866913257104605184 |
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| author | Bernardi, Enrico Lanconelli, Alberto Lauria, Christopher S. A. |
| author_facet | Bernardi, Enrico Lanconelli, Alberto Lauria, Christopher S. A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04345 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Novel Theoretical Framework for Exponential Smoothing Bernardi, Enrico Lanconelli, Alberto Lauria, Christopher S. A. Methodology Probability Machine Learning 65K05, 62F12 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. |
| title | A Novel Theoretical Framework for Exponential Smoothing |
| topic | Methodology Probability Machine Learning 65K05, 62F12 |
| url | https://arxiv.org/abs/2403.04345 |