LGTD: Local-Global Trend Decomposition for Season-Length-Free Time Series Analysis

Chainarong Amornbunchornvej; Chotanansub Sophaken; Piyanon Charoenpoonpanich; Thanadej Rattanakornphan; Thanapol Phungtua-eng

REVIEW 5 major objections 4 minor 17 references

LGTD: Local-Global Trend Decomposition for Season-Length-Free Time Series Analysis

T0 review · 5 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read LGTD proposes that seasonality can be modeled as recurring local trend regimes, eliminating the need for any season-length input.

desk verdict Interesting idea, but the paper's own tables contradict its central accuracy claims; major revision needed. read the letter →

arxiv 2601.04820 v2 pith:HO6QSJSW submitted 2026-01-08 cs.DB cs.SI

Chotanansub Sophaken , Thanadej Rattanakornphan , Piyanon Charoenpoonpanich , Thanapol Phungtua-eng , Chainarong Amornbunchornvej This is my paper · ORCID

classification cs.DBcs.SI

keywords timeseriesdecompositionseasonality-freelocaltrendemergentseasonalitypiecewiselinearsegmentationlinear-timealgorithmnonstationaryperiods

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that seasonal structure in a time series can be treated as an emergent byproduct of recurring local linear trends, rather than as an explicit periodic component. It introduces LGTD, which fits a smooth global trend, segments the detrended series into piecewise-linear local regimes via an error-driven procedure, and uses the reconstruction of those regimes as the seasonal component. The authors prove that this local-trend procedure terminates in a bounded number of iterations and runs in linear time, and they report empirical results where LGTD achieves the lowest average error on synthetic benchmarks across fixed, transitive, and variable season-length settings, while several period-based baselines degrade. The motivation is automated, low-touch decomposition for heterogeneous collections where cycles drift, appear intermittently, or operate at multiple scales.

What carries the argument

The load-bearing component is AutoTrend-LLT, an iterative error-driven segmentation procedure. It maintains a focus set of indices, groups them into contiguous ranges, fits a linear model on a fixed-size window (w=3) immediately preceding each range, extrapolates across the range, and assigns points whose absolute prediction error falls below a percentile threshold. The threshold starts at a baseline percentile and optionally increases by a step Δp each iteration; clamping at p≥100 guarantees all remaining points are assigned, yielding a finite-termination bound K* = 1 + ⌈(100 - p0)/Δp⌉ and an overall runtime of O(K*T). The reconstruction r̂_t from this procedure becomes the local-trend comp

What would settle it

Take a series whose seasonal component is smooth and sinusoidal with a known period but no piecewise-linear structure (for example, a pure sine wave with small noise), run LGTD, and check whether the seasonal component recovers the sine shape or whether the residual retains strong periodic autocorrelation. If the residual still shows the period, the claim that local trend regimes capture emergent seasonality fails.

Watch

Extended reading notes

Core claim

LGTD's central claim is that the decomposition y_t = g_t + l_t + ε_t, with l_t defined as the local-trend reconstruction of the detrended residuals, is a valid season-length-free decomposition. Seasonality is not encoded as a periodic basis; it emerges when similar local trend regimes recur over time. On synthetic data with known ground-truth components, the paper reports the lowest average overall MAE (4.00) compared with all baselines, and the best or near-best seasonal error in transitive and variable-period settings, while methods that rely on a fixed or estimated season length show larger errors as periodicity drifts. On real-world electricity-load and sunspot series, LGTD produces smoo

Load-bearing premise

The decomposition's validity rests on assuming that a piecewise-linear local reconstruction with fixed window w=3 and a percentile-threshold schedule captures the true seasonal structure of the detrended residual; if that segmentation does not align with the actual periodic component, the season-length-free claim collapses.

Editorial extensions

If this is right

Because no season-length parameter is needed, LGTD can serve as a drop-in preprocessing step for heterogeneous time-series collections without per-series tuning.
The finite-termination guarantee, independent of any seasonal parameter, supports use in large-scale or streaming pipelines with predictable linear-time behavior.
In settings where the period shifts mid-series or drifts continuously, LGTD adapts its seasonal component to the changing structure, whereas period-based methods show leakage between seasonal and residual components.
LGTD produces low-structure residuals, which the paper argues can reduce false positives in downstream anomaly-detection and change-point-detection pipelines caused by misspecified seasonality.
The method's runtime is linear in series length and independent of season length, making it faster than baselines that scale super-linearly as periods grow.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If emergent seasonality proves to be a workable characterization, then explicit season-length estimation as a preprocessing step may become unnecessary for a broad class of downstream tasks; one could test this by comparing anomaly-detection false-positive rates on LGTD residuals versus STL-based residuals across datasets with drifting periods.
The linear-time, parameter-free design suggests a natural online variant that maintains the focus set and percentile threshold incrementally, potentially achieving constant-time updates per new observation without a period parameter.
A testable extension is to run LGTD on series with two independent superimposed periodicities and measure whether the local-trend component separates them or conflates them; the paper's experiments use single seasonality regimes, leaving multi-scale separation open.
Because the seasonal component is identified with a local reconstruction rather than a periodic template, LGTD may be better suited to change-point detection than to forecasting, which usually requires an explicit extrapolation rule for future seasonal behavior.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: LGTD's core idea is genuinely interesting — treating seasonality as recurring local trend regimes found by an error-driven, piecewise-linear segmentation, so no season-length parameter is needed. The specific AutoTrend-LLT procedure (forward local linear extrapolation with percentile-threshold reassignment) is new to me in this form, and the framing is a fresh take on a real operational problem. The paper is honest that it's a close relative of piecewise-linear trend and change-point segmentation; that's fine.

The evidence, however, does not hold up, and the problems are load-bearing. Table 1 reports LGTD average MAEs of 3.62 / 4.84 / 3.55 / 4.00 across the nine synthetic datasets. Table 5, reporting the same nine datasets in detail, averages to roughly 4.03 / 7.51 / 6.16 / 5.90. These are not rounding differences. Since Table 1 is the basis for the 'balanced accuracy' claim, the flagship empirical result is unsupported. On fixed-period data, LGTD's seasonal MAE is 2.90–7.40 against STL's 0.28–0.35, so 'balanced' isn't what the detail shows either.

The scalability claim is likewise unbacked. The abstract says linear runtime/memory and 'fastest method' are 'confirmed empirically,' but Section 5 contains no runtime or memory experiment. The complexity analysis (O(K* · T), K* bounded by the percentile schedule) is fine as a theoretical bound — and the termination proof is trivial, since clamping the percentile to 100 assigns everyone — but it is not an empirical confirmation.

The abstract also promises 'a single fixed default configuration.' Table 4 shows LGTD's error percentile varying between 30 and 40 (40 for all real-world sets). That directly contradicts the low-touch selling point.

Conceptually, 'emergent seasonality' is definitional: Section 3.2 sets ℓ_t := r̂_t, so the seasonal component is the local-trend reconstruction by construction. This could still be a useful decomposition for downstream tasks like anomaly detection, but the paper never validates the local-trend proxy against any independent notion of periodicity, and comparing it to STL's periodic component on ground-truth synthetic seasonality stacks the deck in LGTD's favor.

Who gets value: readers working on fully automated, season-length-free decomposition for large heterogenous series will find the idea worth thinking about. But as submitted, the paper is not publishable. It needs a revised evaluation — correct averages, real timing runs, explicit hyperparameter settings, and a clear statement of what the local-trend component does and does not capture. I would send it to referees, because the underlying approach is worth scrutiny and the flaws are fixable, but I'd expect major revision and would not trust the current numbers.

Recommendation: send to peer review with a note that the authors must reconcile Tables 1 and 5 and add the missing experiments before this can be accepted.

Referee Report

5 major / 4 minor

Summary. LGTD is a season-length-free time series decomposition method. It fits a smooth global trend g, applies an error-driven local linear segmentation (AutoTrend-LLT) to the detrended series, defines the seasonal component as the local-trend reconstruction (ℓ_t := r̂_t), and treats the remainder as residuals. The paper claims finite termination, linear-time complexity, empirically confirmed speed/memory advantages, and balanced decomposition accuracy on synthetic and real datasets with fixed, transitive, and variable season lengths. Experiments are reported on nine synthetic datasets and on ETTh1/ETTh2 and sunspot data.

Significance. If the claims were supported, the paper would address a real practical pain point: eliminating season-length specification while maintaining decomposition quality at scale. The algorithmic description is clear, the code and data are promised open source, and the simple complexity analysis is reasonable. However, the central empirical claims are undercut by internal numerical contradictions, a definitional circularity in the 'emergent seasonality' concept, and the absence of the advertised runtime/memory experiments. A method whose seasonal component is defined as the local-trend reconstruction may be useful as a trend-residual segmentation, but the paper does not currently demonstrate that it is a competitive seasonal-trend decomposition.

major comments (5)

[Tables 1–3 vs Table 5] The headline averages in Tables 1–3 are inconsistent with the detailed per-dataset results in Table 5. Averaging LGTD's MAE over the nine synthetic rows of Table 5 gives trend≈4.03, seasonal≈7.51, residual≈6.16, overall≈5.90, not the 3.62/4.84/3.55/4.00 reported in Table 1. Likewise, the transitive-period averages in Table 2 (2.04/4.06/2.83/2.98) and the variable-period averages in Table 3 (7.63/7.78/5.33/6.91) do not match the Table 5 transitive rows (≈2.12/6.39/5.50/4.67) or variable rows (≈8.67/10.50/7.43/8.87). Since the central claim that LGTD achieves the lowest overall MAE and balanced accuracy rests on these averages, the reported evidence does not support it.
[Table 5, fixed-period rows] Even taking Table 5 at face value, LGTD's fixed-period seasonal accuracy is much worse than that of standard STL: on Linear-Fixed, Inverted-V-Fixed, and Piecewise-Fixed, LGTD seasonal MAE is 2.90, 7.35, and 6.65, versus STL's 0.32, 0.28, and 0.33. The component-averaged overall MAE on these fixed-period datasets is approximately 2.2, 5.3, and 5.0 for LGTD versus 0.24, 0.27, and 0.42 for STL. This directly contradicts the abstract and Section 5.1 claim of 'balanced accuracy across fixed, transitive, and variable season-length regimes,' and it undermines the claim that emergent reconstruction is competitive where periodicity is stable.
[Abstract; Section 5] The abstract states 'we confirm this empirically: LGTD scales linearly in runtime and memory and is the fastest method across all tested lengths, while several baselines degrade super-linearly.' No runtime or memory experiment is described in Section 4.4 (which defines only MAE/MSE evaluation) or reported anywhere in Section 5. The scalability claims are therefore unsupported by the manuscript's experimental content. If such experiments exist in the repository, they need to be included in the paper.
[Table 4] The abstract claims LGTD 'operates with a single fixed default configuration across datasets,' but Table 4 shows LGTD's Error Percentile is dataset-dependent: 30 for s1 and s3–s9 but 40 for s2, ETTh1, ETTh2, and sunspot. Section 5.4 also describes AutoTrend as 'parameter-free' while acknowledging internal hyperparameters (p0, Δp, w, Kmax). The paper should clarify the distinction between not requiring a season length and being hyperparameter-free; as written, the fixed-configuration marketing claim is contradicted by the reported configuration table.
[Section 3.2, Algorithm 2] The 'emergent seasonality' claim is definitional rather than demonstrated. Algorithm 2 sets ℓ_t := r̂_t, so the seasonal component is by construction the LLT reconstruction (Section 3.2: 'local-trend component is identified with the LLT reconstruction'). The statement that recurring local-trend regimes 'act as emergent seasonality' is therefore tautological unless the reconstruction is independently shown to correspond to the underlying seasonal structure. The evidence in Table 5 (fixed-period rows) suggests it does not. Similarly, Proposition 3.1's termination bound is a direct consequence of the percentile clamp—once p≥100, the threshold becomes max(E) and all remaining focus points are assigned. It is correct but does not validate the segmentation's meaningfulness.

minor comments (4)

[Section 5.1, text before Table 2] The sentence 'Results for datasets with stable season length are shown in Table 2' is inconsistent with Table 2's title ('Transitive Period Datasets') and with Section 4.2.2, which defines a transitive period as a mid-series transition. Please reconcile the terminology.
[Section 5.4] Calling AutoTrend 'parameter-free' because it does not require a seasonal period is misleading. Recommend using 'period-free' or 'period-agnostic' and explicitly listing w, p0, Δp, Kmax, and update_threshold as tunable hyperparameters.
[Table 4] RobustSTL is configured with Period=12 for all synthetic datasets, while the ground-truth periods are 120 or 60. If this is intentional, explain why; otherwise, this configuration likely disadvantages RobustSTL in a way unrelated to LGTD's contribution.
[Algorithm 1 and Section 3.3] The complexity analysis assumes K* iterations with Kmax ≥ K*, but the algorithm can terminate early with unassigned points if Kmax is smaller. State explicitly what happens when Kmax < K* or when the focus set is not empty after Kmax iterations.

Circularity Check

1 steps flagged · score 4.0 of 10

Seasonal component is stipulated as the local-trend reconstruction (ℓ := r̂), so the headline 'emergent seasonality' claim is definitional; the core algorithm and proofs are otherwise self-contained, with separately serious but non-circular empirical inconsistencies.

self definitional [Section 3.2 (Local Trend Extraction / Emergent Seasonality); Algorithm 2 Step 3]
"In the LGTD decomposition, the local-trend component is identified with the LLT reconstruction, i.e., ℓ_t := r̂_t, so that recurring local-trend regimes act as emergent seasonality even when timing is irregular or drifting."

The component labeled 'seasonal' is defined to be exactly the output of AutoTrend-LLT on the detrended residual. Therefore the paper's central conceptual claim that seasonality 'emerges' from recurring local-trend regimes is true by stipulation rather than by independent derivation: if the reconstruction were instead named 'local fluctuations,' no seasonal claim would follow. The synthetic evaluation then compares this stipulated component to ground-truth periodic seasonal signals, so the accuracy numbers can fail and are not themselves forced; but the 'emergent seasonality' framing reduces to the definition ℓ := r̂ rather than being a derived first-principles result.

full rationale

The algebraic decomposition y_t = g_t + ℓ_t + ε_t with ε_t := y_t − g_t − ℓ_t is an identity by construction, so calling the remainder a 'residual' is definitional but not a hidden circular prediction. Similarly, the 'season-length-free' property follows directly from the absence of any period parameter in Algorithms 1–2; that is a design feature, not a derived empirical law. The finite-termination bound (Proposition 3.1) is a direct consequence of the percentile schedule reaching p ≥ 100 together with the clamped percentile assumption; it is a valid but near-tautological algorithmic proof, not a data-driven discovery, so I did not count it as a separate circular step. No load-bearing self-citation appears: the co-authored ASTD reference [9] is used only as a baseline, and the paper does not invoke a uniqueness theorem or prior work to justify its central decomposition. However, the manuscript has serious non-circular empirical problems that should be weighed separately: Table 1's LGTD averages (Trend 3.62, Seasonal 4.84, Residual 3.55, Overall 4.00) are inconsistent with Table 5's component-wise values, which imply averages of about 4.03 / 7.51 / 6.16 and an overall near 5.90; the abstract's 'single fixed default configuration' is contradicted by Table 4, where LGTD's Error Percentile is set to 30 or 40 per dataset; and the claimed empirical confirmation of 'linear scaling' and 'fastest method' is not supported by any runtime or memory experiment in Section 5. These inconsistencies undermine confidence in the balanced-accuracy and scalability claims but are not circularity under the review criteria.

Assumptions & free parameters 5 free parameters · 3 assumptions · 1 invented entities

LGTD's contribution rests on several free hyperparameters that are incompletely specified, on the unvalidated assumption that piecewise-linear local regimes can stand in for genuine periodic structure, and on the definitional move that identifies the seasonal component with the local-trend reconstruction.

free parameters (5)

Window size w = 3
Fixed window for local linear regressions; arbitrary and not justified by data (Table 4).
Baseline percentile p0 = 30 (synthetic), 40 (real)
Error percentile threshold controlling segmentation; varies across dataset groups, contradicting the single-fixed-default claim (Table 4).
Percentile step Δp = Not reported
Controls the termination bound K★ and segmentation behavior; not listed in Table 4, so experiments are not fully reproducible.
Max iterations Kmax = Not reported
Termination cap for AutoTrend-LLT; not listed in Table 4.
Global trend model G and θg = Unspecified
The paper allows 'any regression or smoothing model' but never states which G was used in the experiments; a load-bearing modeling choice.

assumptions (3)

ad hoc to paper Seasonality is adequately represented by recurrence of piecewise-linear local trend regimes
This is the conceptual core (Section 3.2) and is assumed, not derived or validated on independent data.
domain assumption The detrended series can be segmented by error-driven percentile assignment with fixed window w=3
Algorithm 1 assumes local linear extrapolation from a small preceding window predicts future values well enough to partition the series into meaningful regimes.
domain assumption The first w points need not receive a local-trend label
Algorithm 1 initializes the focus set as {w,...,T-1}, silently excluding the first w points from local-trend decomposition.

invented entities (1)

Emergent seasonality (seasonal component redefined as local-trend reconstruction)
purpose: Allows LGTD to claim season-length-free decomposition without explicitly modeling periodic structure
The seasonal component is defined as ℓ_t := r̂_t (Section 3.2); no independent verification that reconstructed local trends correspond to true seasonality beyond synthetic MAE values.

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Cite this review

Pith. "Pith review of LGTD: Local-Global Trend Decomposition for Season-Length-Free Time Series Analysis." pith.science (2026). https://pith.science/paper/HO6QSJSW

@misc{pith2026260104820,
  author       = {Pith},
  title        = {Pith review of: LGTD: Local-Global Trend Decomposition for Season-Length-Free Time Series Analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HO6QSJSW}},
  note         = {Machine review of arXiv:2601.04820}
}

read the original abstract

Time series decomposition into trend, seasonal, and residual components is a fundamental primitive in data mining and analytics pipelines, underpinning anomaly detection, change-point analysis, and forecasting. Most existing methods require a user-specified or estimated season length and assume stable periodic structure. In large, heterogeneous collections, where recurring patterns drift, appear intermittently, or operate at multiple nonstationary scales, period selection becomes brittle and per-series tuning does not scale. We propose LGTD (Local-Global Trend Decomposition), a season-length-free decomposition framework that requires no period specification and operates with a single fixed default configuration across datasets. LGTD represents a series as the sum of (i) a smooth global trend capturing long-term evolution, (ii) adaptive local trends inferred by an error-driven local linear segmentation procedure, and (iii) a residual component. Rather than modeling seasonality through an explicit periodic basis, LGTD treats it as an emergent property arising from the recurrence of local trend regimes, decoupling decomposition quality from any estimated season length. We prove that the local trend inference procedure terminates in a bounded number of iterations and runs in linear time in the series length, independent of any seasonal parameter, and confirm this empirically: LGTD scales linearly in runtime and memory and is the fastest method across all tested lengths, while several baselines degrade super-linearly. On synthetic benchmarks LGTD achieves balanced accuracy across fixed, transitive, and variable season-length regimes, particularly where period-based methods degrade, and on real-world data it yields interpretable components and low-structure residuals. Source code and datasets are available at https://github.com/chotanansub/LGTD.

Figures

Figures reproduced from arXiv: 2601.04820 by the authors.

**Figure 1.** LGTD global–local decomposition process. After estimating a global trend 𝑔𝑡 , the detrended series is segmented adaptively by AutoTrend-LLT to discover local trends ℓ𝑡 , which serve as emergent seasonal components without requiring a predefined season length. Removing both trends yields final residuals 𝜀𝑡 , giving the decomposition 𝑦𝑡 = 𝑔𝑡 + ℓ𝑡 + 𝜀𝑡 . underlying events or regime transitions. This perspective suggest… view at source ↗

**Figure 2.** Decomposition on transitive season-length data, [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 4.** Decomposition of the ETTh1 dataset, showing that [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

Figures from the paper (2 more)

**Figure 5.** Figure 5: Decomposition of the SILSO sunspot series, showing [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: Decomposition comparisons across all nine synthetic datasets. Each panel shows the original time series and extracted [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

17 extracted references · 2 canonical work pages

[1]

Kasun Bandara, Rob J Hyndman, and Christoph Bergmeir. 2021. MSTL: A Seasonal-Trend Decomposition Algorithm for Time Series with Multiple Seasonal Patterns. arXiv:2107.13462 [stat.AP] https://arxiv.org/abs/2107.13462

arXiv 2021
[2]

Zijie Chen, Shaoxu Song, and Jianmin Wang. 2025. OneRoundSTL: In-Database Seasonal-Trend Decomposition. In2025 IEEE 41st International Conference on Data Engineering (ICDE). 1–13. https://doi.org/10.1109/ICDE65448.2025.00060

arXiv 2025
[3]

Frédéric Clette and Laure Lefèvre. 2015. SILSO Sunspot Number Version 2.0. https://doi.org/10.24414/qnza-ac80 Accessed via WDC-SILSO

doi:10.24414/qnza-ac80 2015
[4]

Robert B Cleveland, William S Cleveland, Jean E McRae, Irma Terpenning, et al
[5]

Alexander Dokumentov and Rob J Hyndman. 2022. STR: Seasonal-trend de- composition using regression.INFORMS Journal on Data Science1, 1 (2022), 50–62

2022
[6]

Xiao He, Ye Li, Jian Tan, Bin Wu, and Feifei Li. 2023. OneShotSTL: One-Shot Seasonal-Trend Decomposition For Online Time Series Anomaly Detection And Forecasting.Proc. VLDB Endow.16, 6 (Feb. 2023), 1399–1412. https://doi.org/10. 14778/3583140.3583155

arXiv 2023
[7]

Seung-Jean Kim, Kwangmoo Koh, Stephen Boyd, and Dimitry Gorinevsky. 2009. ℓ1 Trend Filtering.SIAM Rev.51, 2 (May 2009), 339–360. https://doi.org/10.1137/ 070690274

2009
[8]

Abhinav Mishra, Ram Sriharsha, and Sichen Zhong. 2022. OnlineSTL: scaling time series decomposition by 100x.Proc. VLDB Endow.15, 7 (March 2022), 1417–1425. https://doi.org/10.14778/3523210.3523219

arXiv 2022

Show all 17 references

[9]

Thanapol Phungtua-eng and Yoshitaka Yamamoto. 2024. Adaptive Seasonal- Trend Decomposition for Streaming Time Series Data with Transitions and Fluctuations in Seasonality. InMachine Learning and Knowledge Discovery in Databases. Research Track: European Conference, ECML PKDD 2...

2024 doi
[10]

Tom Puech, Matthieu Boussard, Anthony D’Amato, and Gaëtan Millerand. 2020. A Fully Automated Periodicity Detection in Time Series. InAdvanced Analytics and Learning on Temporal Data, Vincent Lemaire, Simon Malinowski, Anthony Bagnall, Alexis Bondu, Thomas Guyet, and Romain Tav...

2020
[11]

Maximilian Toller, Tiago Santos, and Roman Kern. 2019. SAZED: parameter-free domain-agnostic season length estimation in time series data.Data Mining and Knowledge Discovery33, 6 (01 Nov 2019), 1775–1798. https://doi.org/10.1007/ s10618-019-00645-z

2019
[12]

Michail Vlachos, Philip Yu, and Vittorio Castelli. [n. d.]. On Periodicity Detection and Structural Periodic Similar- ity. 449–460. https://doi.org/10.1137/1.9781611972757.40 arXiv:https://epubs.siam.org/doi/pdf/10.1137/1.9781611972757.40

doi
[13]

Haoyu Wang, Hongke Guo, Zhaoliang Zhu, You Zhang, Yu Zhou, and Xudong Zheng. 2024. BacktrackSTL: Ultra-Fast Online Seasonal-Trend Decomposition with Backtrack Technique. InProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining(Barcelona, Spain)(KD...

2024
[14]

Qingsong Wen, Jingkun Gao, Xiaomin Song, Liang Sun, Huan Xu, and Shenghuo Zhu. 2019. RobustSTL: a robust seasonal-trend decomposition algorithm for long time series. InProceedings of the Thirty-Third AAAI Conference on Artificial Intel- ligence and Thirty-First Innovative Appl...

2019
[15]

Qingsong Wen, Zhe Zhang, Yan Li, and Liang Sun. 2020. Fast RobustSTL: Ef- ficient and Robust Seasonal-Trend Decomposition for Time Series with Com- plex Patterns. InProceedings of the 26th ACM SIGKDD International Confer- ence on Knowledge Discovery & Data Mining(Virtual Event...

2020
[16]

Haoyi Zhou, Shanghang Zhang, Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, and Wancai Zhang. 2021. Informer: Beyond Efficient Transformer for Long Se- quence Time-Series Forecasting. InThe Thirty-Fifth AAAI Conference on Artificial Intelligence, AAAI 2021, Virtual Conference...

2021
[1990]

STL: A seasonal-trend decomposition.J. off. Stat6, 1 (1990), 3–73

1990

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

[1] [1]

Kasun Bandara, Rob J Hyndman, and Christoph Bergmeir. 2021. MSTL: A Seasonal-Trend Decomposition Algorithm for Time Series with Multiple Seasonal Patterns. arXiv:2107.13462 [stat.AP] https://arxiv.org/abs/2107.13462

arXiv 2021

[2] [2]

Zijie Chen, Shaoxu Song, and Jianmin Wang. 2025. OneRoundSTL: In-Database Seasonal-Trend Decomposition. In2025 IEEE 41st International Conference on Data Engineering (ICDE). 1–13. https://doi.org/10.1109/ICDE65448.2025.00060

arXiv 2025

[3] [3]

Frédéric Clette and Laure Lefèvre. 2015. SILSO Sunspot Number Version 2.0. https://doi.org/10.24414/qnza-ac80 Accessed via WDC-SILSO

doi:10.24414/qnza-ac80 2015

[4] [4]

Robert B Cleveland, William S Cleveland, Jean E McRae, Irma Terpenning, et al

[5] [5]

Alexander Dokumentov and Rob J Hyndman. 2022. STR: Seasonal-trend de- composition using regression.INFORMS Journal on Data Science1, 1 (2022), 50–62

2022

[6] [6]

Xiao He, Ye Li, Jian Tan, Bin Wu, and Feifei Li. 2023. OneShotSTL: One-Shot Seasonal-Trend Decomposition For Online Time Series Anomaly Detection And Forecasting.Proc. VLDB Endow.16, 6 (Feb. 2023), 1399–1412. https://doi.org/10. 14778/3583140.3583155

arXiv 2023

[7] [7]

Seung-Jean Kim, Kwangmoo Koh, Stephen Boyd, and Dimitry Gorinevsky. 2009. ℓ1 Trend Filtering.SIAM Rev.51, 2 (May 2009), 339–360. https://doi.org/10.1137/ 070690274

2009

[8] [8]

Abhinav Mishra, Ram Sriharsha, and Sichen Zhong. 2022. OnlineSTL: scaling time series decomposition by 100x.Proc. VLDB Endow.15, 7 (March 2022), 1417–1425. https://doi.org/10.14778/3523210.3523219

arXiv 2022