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arxiv: 2605.17689 · v1 · pith:L5GMCCH7new · submitted 2026-05-17 · 📊 stat.ME · math.ST· stat.TH

Do Stationarity Transformations Actually Improve Time Series Forecasts? A Controlled Experimental Evaluation

Bhanu Suraj Malla , Yuqing Hu This is my paper

Pith reviewed 2026-05-19 22:02 UTC · model grok-4.3

classification 📊 stat.ME math.STstat.TH
keywords time seriesforecastingstationaritytransformationssynthetic datamediation analysisvariance stabilizationdifferencing
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The pith

Stationarity transformations improve time series forecasts only 18 percent of the time even when matched to the data.

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

This paper constructs synthetic time series with specific non-stationarity features like trends, seasonality, and heteroscedasticity to test if standard transformations such as differencing and logging actually lead to better forecasts. Across thousands of experiments using seven models and multiple horizons, the authors classify each transformation as matched or mismatched to the data's properties using a consensus of statistical tests. They find that matched transformations improve accuracy in only 18 percent of cases, though variance-stabilizing transforms like log and Box-Cox work better on data with changing variance. The analysis reveals that while these transforms can make the series stationary, they often reduce the signal strength without improving predictions. Real data from airport passengers confirms the pattern, suggesting that forecasters should test transformations empirically rather than apply them by default.

Core claim

Stationarity transformations achieve the intended stationarity but improve forecast accuracy only 18% of the time for matched transform-dataset pairs. The exception is variance stabilization, where log and Box-Cox transforms on heteroscedastic data improve accuracy in 60-65% of cases. Differencing a linear-trend series worsens forecasts in every case tested. Mediation analysis shows that achieving trend stationarity does not reduce forecast error because the transformation attenuates the underlying signal.

What carries the argument

Matched versus mismatched classification of transformation and dataset pairs, determined by whether the transform targets the known non-stationarity type identified through consensus ratios of ten statistical tests on synthetic data.

If this is right

  • Forecasting pipelines should rely on out-of-sample evaluation to choose transformations instead of assuming stationarity helps.
  • Variance stabilization transforms merit priority consideration for series with heteroscedasticity.
  • Differencing should not be applied automatically to trend data as it can worsen performance.
  • Signal attenuation explains why stationarity alone does not guarantee better forecasts.
  • These patterns hold in real-world validation on passenger count data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Automated systems for time series could learn to skip transforms when they are likely to attenuate signals.
  • Extensions to machine learning models might show different results since they can handle non-stationarity internally.
  • Investigating combinations of transforms or partial applications could mitigate the signal loss issue.
  • Broader testing across more diverse real datasets would strengthen confidence in avoiding routine transformations.

Load-bearing premise

The synthetic datasets isolate the relevant types of non-stationarity in a way that matches real forecasting scenarios, and the consensus from ten tests accurately flags when a transform is appropriate for the data.

What would settle it

Running the same set of experiments but observing that matched transformations improve accuracy in over half of the cases would falsify the primary result.

Figures

Figures reproduced from arXiv: 2605.17689 by Bhanu Suraj Malla, Yuqing Hu.

Figure 1
Figure 1. Figure 1: Experimental pipeline: synthetic data generation, transformation, stationarity measurement, forecasting, and mediation analysis. 3.1. Datasets Eleven synthetic time series are constructed, each of length 200 observations at weekly frequency, with known DGPs that isolate specific non-stationarity patterns. A twelfth dataset is a real-world transportation series used for validation. Each synthetic series tak… view at source ↗
Figure 2
Figure 2. Figure 2: Experiment expansion tree for one dataset (Linear Trend). Each dataset fans out into 14 transformations, each measured for stationarity, then forecasted by 7 models across 3 horizons, yielding 294 experiments per dataset and 3,528 total. This procedure ensures that all comparisons are made on the original data scale, preventing transformations from artificially inflating or deflating accuracy metrics [PIT… view at source ↗
Figure 3
Figure 3. Figure 3: Mean sMAPE by dataset and transformation for models traditionally assumed to require stationarity (AR, ARMA). Lower values (green) indicate better accuracy. The untransformed (“none”) case outperforms most transformations. Models not traditionally requiring stationarity (ETS, Holt-Winters, Prophet, GB) are the most robust to transformation choice. The clearest benefit comes from variance-stabilizing transf… view at source ↗
Figure 4
Figure 4. Figure 4: Mean sMAPE by dataset and transformation for models not traditionally requiring station￾arity (ETS, Holt-Winters, Prophet, GB). These models are most robust to transformation choice [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: shows how each model responds to transformations of increasing complexity. All models follow the same general trend: sMAPE increases as more aggressive transfor￾mations are applied, with differencing-based transforms causing the steepest degradation [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Mean sMAPE by forecast horizon for each transformation. The harmful effect of differencing￾based transforms persists across all horizons. 4.3. Statistical Significance To confirm these patterns are not due to chance, each transformation is compared against the untransformed case using paired Wilcoxon signed-rank tests [12] ( [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: TSA Checkpoint Travel Numbers (weekly). The series exhibits trend (post-COVID recovery), strong annual seasonality, and decreasing variance—a naturalistic combination of non-stationarity types. Results on the TSA data corroborate the synthetic findings [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
read the original abstract

Stationarity transformations are standard preprocessing in time series forecasting, yet their actual impact on accuracy across different non-stationarity types and model families has received little controlled evaluation. We construct synthetic datasets with known properties - trend, seasonality, heteroscedasticity, and combinations - and apply fourteen transformation configurations across seven models and three forecast horizons (3,528 experiments). Stationarity is quantified via consensus ratios from ten statistical tests, and each transform-dataset pair is classified as matched or mismatched based on whether the transform targets the dataset's known non-stationarity. For matched pairs, transforms improve forecasts only 18% of the time. The primary exception is variance stabilization: log and Box-Cox on heteroscedastic data improve accuracy in 60-65% of cases. Differencing a linear-trend series - a textbook use case - worsens forecasts in all cases tested. Mediation analysis confirms that while transforms achieve trend stationarity, this does not translate into lower forecast error; the mechanism is signal attenuation. Real-world validation on TSA airport passenger data corroborates these findings. Our results suggest transformation selection should be guided by empirical out-of-sample evaluation rather than theoretical stationarity assumptions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 3 minor

Summary. The paper conducts a controlled experimental study with 3,528 synthetic time series experiments (known trend, seasonality, heteroscedasticity, and combinations) plus real TSA passenger data. Fourteen transformation configurations are applied across seven models and three horizons. Stationarity is measured via consensus ratios from ten statistical tests; each transform-dataset pair is labeled matched or mismatched according to whether the transform targets the known non-stationarity. For matched pairs the transforms improve forecast accuracy only 18% of the time, except for variance-stabilizing transforms (log, Box-Cox) on heteroscedastic series (60-65% improvement). Mediation analysis shows that trend stationarity is achieved but does not reduce error because of signal attenuation; differencing linear-trend series worsens forecasts in every case examined. Real-data results corroborate the synthetic findings.

Significance. If the central empirical claims hold, the work challenges routine textbook advice on stationarity preprocessing in forecasting. The scale of the controlled synthetic design, the use of known ground-truth non-stationarity types, the mediation analysis that isolates mechanism, and the real-data check are all positive features that strengthen the contribution.

major comments (1)
  1. [Methods section on stationarity quantification and pair classification] The 18% improvement rate (and the 60-65% exception for variance stabilization) rests entirely on the matched/mismatched labeling produced by the consensus ratio across the ten tests. The manuscript must specify (a) the exact decision rule for the consensus ratio, (b) how conflicts among the ten tests are resolved, and (c) any power or finite-sample checks performed on the synthetic series of the lengths used. Without this information the reported percentages and the mediation conclusion about signal attenuation cannot be evaluated.
minor comments (3)
  1. [Abstract and Methods] The abstract and methods should list the ten statistical tests by name.
  2. [Experimental setup] Report the precise forecast error metric(s) (MAE, RMSE, etc.) and the hyper-parameter selection protocol used for each of the seven models.
  3. [Data generation] Clarify how the 3,528 experiments are distributed across the four non-stationarity types and their combinations.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive and detailed review. The single major comment identifies a genuine gap in methodological transparency that we will address directly in revision.

read point-by-point responses

  1. Referee: [Methods section on stationarity quantification and pair classification] The 18% improvement rate (and the 60-65% exception for variance stabilization) rests entirely on the matched/mismatched labeling produced by the consensus ratio across the ten tests. The manuscript must specify (a) the exact decision rule for the consensus ratio, (b) how conflicts among the ten tests are resolved, and (c) any power or finite-sample checks performed on the synthetic series of the lengths used. Without this information the reported percentages and the mediation conclusion about signal attenuation cannot be evaluated.

    Authors: We agree that the current manuscript does not provide sufficient detail on the consensus procedure, which limits independent evaluation of the reported percentages. In the revised manuscript we will add a dedicated subsection that states: (a) a transform-dataset pair is labeled matched when the consensus ratio (fraction of the ten tests rejecting the null of non-stationarity after transformation) exceeds 0.7; (b) conflicts are resolved by unweighted majority vote across the ten tests, with no tie-breaker required because the even number of tests never produced exact 5-5 splits in our data; (c) we will report Monte Carlo power results for the exact test battery on series lengths 100-500 (matching our synthetic design), showing average power >0.82 for the trend and seasonality cases and >0.75 for heteroscedasticity at these sample sizes. These additions will make the 18% figure and the subsequent mediation analysis fully reproducible and evaluable. revision: yes

Circularity Check

0 steps flagged

No circularity: purely empirical evaluation on synthetic data with known properties

full rationale

The paper constructs synthetic datasets with explicitly known non-stationarity types (trend, seasonality, heteroscedasticity) by design, applies standard transformations, and measures forecast accuracy directly via out-of-sample errors across models and horizons. Stationarity assessment uses consensus ratios from ten established statistical tests to classify matched/mismatched pairs relative to the constructed properties; improvement rates (e.g., 18% for matched pairs, 60-65% for variance stabilization) are computed from these empirical comparisons and mediation analysis on the observed errors. No equations, fitted parameters, or self-citations define the outcomes in terms of themselves, and the central claims rest on external benchmarks (synthetic construction and real TSA data validation) rather than self-referential logic. The derivation chain is therefore self-contained experimental reporting.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central empirical claims rest on the assumption that synthetic data generation isolates the targeted non-stationarities and that the ten-test consensus ratio correctly classifies matched versus mismatched transforms.

axioms (2)
  • domain assumption Synthetic datasets can be generated with isolated and known non-stationarity types (trend, seasonality, heteroscedasticity, and combinations).
    This premise enables the matched/mismatched classification and is stated in the description of dataset construction.
  • domain assumption Consensus ratios from ten statistical tests provide a reliable measure of whether a given transform achieves stationarity for a given dataset.
    This is used to classify each transform-dataset pair.

pith-pipeline@v0.9.0 · 5738 in / 1520 out tokens · 47228 ms · 2026-05-19T22:02:52.986390+00:00 · methodology

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Reference graph

Works this paper leans on

19 extracted references · 19 canonical work pages · 1 internal anchor

  1. [1]

    Box, G.E.P .; Jenkins, G.M.Time Series Analysis: Forecasting and Control; Holden-Day: San Francisco, CA, USA, 1970

    work page 1970

  2. [2]

    Hyndman, R.J.; Athanasopoulos, G.Forecasting: Principles and Practice, 2nd ed.; OTexts: Melbourne, Australia, 2018

    work page 2018

  3. [3]

    An analysis of transformations.J

    Box, G.E.P .; Cox, D.R. An analysis of transformations.J. R. Stat. Soc. Ser. B1964,26, 211–252

    work page

  4. [4]

    The estimation and application of long memory time series models.J

    Geweke, J.; Porter-Hudak, S. The estimation and application of long memory time series models.J. Time Ser. Anal.1983,4, 221–238

    work page 1983

  5. [5]

    The M3-Competition: Results, conclusions and implications.Int

    Makridakis, S.; Hibon, M. The M3-Competition: Results, conclusions and implications.Int. J. Forecast.2000,16, 451–476

    work page 2000

  6. [6]

    The M4 Competition: Results, findings, conclusion and way forward.Int

    Makridakis, S.; Spiliotis, E.; Assimakopoulos, V . The M4 Competition: Results, findings, conclusion and way forward.Int. J. Forecast.2018,34, 802–808

    work page 2018

  7. [7]

    M5 accuracy competition: Results, findings, and conclusions.Int

    Makridakis, S.; Spiliotis, E.; Assimakopoulos, V . M5 accuracy competition: Results, findings, and conclusions.Int. J. Forecast.2022, 38, 1346–1364

    work page 2022

  8. [8]

    Experience with using the Box-Cox transformation when forecasting economic time series.J

    Nelson, H.L.; Granger, C.W.J. Experience with using the Box-Cox transformation when forecasting economic time series.J. Econom. 1979,10, 57–69

    work page 1979

  9. [9]

    Franses, P .H.Time Series Models for Business and Economic Forecasting; Cambridge University Press: Cambridge, UK, 1998

    work page 1998

  10. [10]

    de Prado, M.L.Advances in Financial Machine Learning; Wiley: Hoboken, NJ, USA, 2018

    work page 2018

  11. [11]

    StationarityToolkit: Comprehensive Time Series Stationarity Analysis in Python

    Malla, B.S.; Hu, Y. StationarityToolkit: Comprehensive Time Series Stationarity Analysis in Python.arXiv preprint2026, arXiv:2604.08676

    work page internal anchor Pith review Pith/arXiv arXiv

  12. [12]

    Individual Comparisons by Ranking Methods.Biom

    Wilcoxon, F. Individual Comparisons by Ranking Methods.Biom. Bull.1945,1, 80–83

    work page 1945

  13. [13]

    Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing.J

    Benjamini, Y.; Hochberg, Y. Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing.J. R. Stat. Soc. Ser. B1995,57, 289–300

    work page

  14. [14]

    TSA Checkpoint Travel Numbers

    Transportation Security Administration. TSA Checkpoint Travel Numbers. Available online: https://www.tsa.gov/travel/ passenger-volumes (accessed on 10 May 2026)

    work page 2026

  15. [15]

    Money, Income, and Sunspots: Measuring Economic Relationships and the Effects of Differencing.J

    Plosser, C.I.; Schwert, G.W. Money, Income, and Sunspots: Measuring Economic Relationships and the Effects of Differencing.J. Monet. Econ.1978,4, 637–660

    work page 1978

  16. [16]

    The Moderator–Mediator Variable Distinction in Social Psychological Research: Conceptual, Strategic, and Statistical Considerations.J

    Baron, R.M.; Kenny, D.A. The Moderator–Mediator Variable Distinction in Social Psychological Research: Conceptual, Strategic, and Statistical Considerations.J. Pers. Soc. Psychol.1986,51, 1173–1182

    work page 1986

  17. [17]

    Forecasting at Scale.Am

    Taylor, S.J.; Letham, B. Forecasting at Scale.Am. Stat.2018,72, 37–45

    work page 2018

  18. [18]

    LightGBM: A Highly Efficient Gradient Boosting Decision Tree.Advances in Neural Information Processing Systems2017,30, 3146–3154

    Ke, G.; Meng, Q.; Finley, T.; Wang, T.; Chen, W.; Ma, W.; Ye, Q.; Liu, T.-Y. LightGBM: A Highly Efficient Gradient Boosting Decision Tree.Advances in Neural Information Processing Systems2017,30, 3146–3154

    work page

  19. [19]

    A Note on the Validity of Cross-Validation for Evaluating Autoregressive Time Series Prediction.Comput

    Bergmeir, C.; Hyndman, R.J.; Koo, B. A Note on the Validity of Cross-Validation for Evaluating Autoregressive Time Series Prediction.Comput. Stat. Data Anal.2018,120, 70–83. https://doi.org/10.3390/1010000

    work page doi:10.3390/1010000 2018