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08-06-2021 | Original Article

Mathematical optimization for time series decomposition

Authors: Seyma Gozuyilmaz, O. Erhun Kundakcioglu

Published in: OR Spectrum | Issue 3/2021

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Abstract

Decomposing time series into trend and seasonality components reveals insights used in forecasting and anomaly detection. This study proposes a mathematical optimization approach that addresses several data-related issues in time series decomposition. Our approach does not only handle longer and multiple seasons but also identifies outliers and trend shifts. Numerical experiments on real-world and synthetic problem sets present the effectiveness of the proposed approach.

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The user can purposefully set M value and limit trend shifts. We highlight even a large number does not lead to an unrealistic solution due to the rest of the constraints.

Similar to the trend shift, the user can set M value if spikes or dips are to be bounded.

The code that solves RobustSTL is available at https://github.com/LeeDoYup/RobustSTL.

The data are available at https://raw.githubusercontent.com/jbrownlee/Datasets/master/daily-min-temperatures.csv.

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Title: Mathematical optimization for time series decomposition
Authors: Seyma Gozuyilmaz
O. Erhun Kundakcioglu
Publication date: 08-06-2021
Publisher: Springer Berlin Heidelberg
Published in: OR Spectrum / Issue 3/2021
Print ISSN: 0171-6468
Electronic ISSN: 1436-6304
DOI: https://doi.org/10.1007/s00291-021-00637-w

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