我们真的在基准测试预测模型吗？预处理对时间序列性能的影响

# Are We Really Benchmarking Forecasting Models? The Impact of Preprocessing on Time Series Performance
Source: [https://arxiv.org/html/2610.09096](https://arxiv.org/html/2610.09096)
Guilherme Afonso Galindo Padilha & Rafael Menelau Oliveira e CruzAffiliation:LIVIA, Department of Software and IT EngineeringAffiliation:École de technologie supérieure \(ÉTS\)Affiliation:Montreal, QC, CanadaEmail:[guilherme\-afonso\.galindo\-padilha\.1@ens\.etsmtl\.ca](mailto:)Email:[rafael\.menelau\-cruz@etsmtl\.ca](mailto:)Paulo Salgado Gomes de Mattos NetoAffiliation:Center for Informatics \(CIn\)Affiliation:Universidade Federal de Pernambuco \(UFPE\)Affiliation:Recife, PE, BrazilEmail:[psgmn@cin\.ufpe\.br](mailto:)

###### Abstract

While established literature underscores the pivotal role of preprocessing in forecasting accuracy, this stage remains largely overlooked in current research\. Modern benchmarks typically resort to simple scaling, failing to account for critical transformations required to address nonstationarity, such as differencing\. This omission creates a significantstructural preprocessing biasthat favors models with built\-in data treatments while obscuring the true potential of simpler architectures\. We study this effect through a preprocessing\-aware benchmark that evaluates 11 forecasting models across 16 reversible preprocessing pipelines on 29,000 M4 time series\. Our results identify preprocessing as a key driver of forecasting performance\. Optimizing preprocessing per series yields gains of approximately 27% to 87% across all evaluated models, with architectures lacking internalized preprocessing experiencing the most substantial improvements\. This allows simpler architectures to become highly competitive with complex, state\-of\-the\-art models in modern forecasting benchmarks\. All resources and experimental results from this benchmark are stored in a comprehensive metadataset to support future metalearning tasks\. Codes111[https://anonymous\.4open\.science/r/patm](https://anonymous.4open.science/r/patm)and data222[https://kaggle\.com/datasets/da12fb43d170e753a639014016fe33742660e87cfcb265b2e9a954186aa7fac5](https://kaggle.com/datasets/da12fb43d170e753a639014016fe33742660e87cfcb265b2e9a954186aa7fac5)are available\.

## 1Introduction

Time series forecasting is a fundamental tool for decision\-making in domains ranging from economics\([Granger and Newbold, 2014](https://arxiv.org/html/2610.09096#bib.bib12)\)and finance\([Tsay, 2005](https://arxiv.org/html/2610.09096#bib.bib11)\)to energy demand\([Deb et al\., 2017](https://arxiv.org/html/2610.09096#bib.bib13)\)and healthcare\([Kaushik et al\., 2020](https://arxiv.org/html/2610.09096#bib.bib14);[Zeroual et al\., 2020](https://arxiv.org/html/2610.09096#bib.bib15)\)\. Because new forecasting methods are typically validated through benchmark comparisons, benchmarks play a central role in shaping research progress, determining which methods are perceived as state of the art, and guiding adoption in practice\. Progress in the field therefore depends not only on developing new forecasting models, but also on the quality, transparency, and fairness of the benchmarks used to evaluate them\.

However, forecasting performance is not determined by model architecture alone\. It also depends on the preprocessing pipeline that transforms the raw time series before training and evaluation\. This issue is especially important for nonstationary time series, which are common in real\-world applications and may exhibit trends, evolving seasonality, or changing variance\. Such properties alter the statistical conditions under which forecasting models are trained and tested\. Many forecasting methods perform best when the input series is closer to stationary, while others incorporate mechanisms that partially compensate for nonstationarity internally\([Liu et al\., 2023](https://arxiv.org/html/2610.09096#bib.bib23);[Salles et al\., 2019](https://arxiv.org/html/2610.09096#bib.bib8);[Hyndman and Athanasopoulos, 2018](https://arxiv.org/html/2610.09096#bib.bib21)\)\.

Figure[1](https://arxiv.org/html/2610.09096#S1.F1)illustrates this dependency through forecasts from an MLP and an ARMA model under different data\-generating regimes\. Without a preprocessing pipeline, both models perform well in the stationary case, but their forecasts deteriorate as nonstationary components such as trend, changing variance, random\-walk behavior, seasonality, or multiple interacting effects are introduced\. Although this example is illustrative rather than a general proof, it highlights a central point of this work: preprocessing choices can materially change the effective difficulty of the forecasting task and, consequently, the apparent performance of different model families\.

![Refer to caption](https://arxiv.org/html/2610.09096v1/figures/stationary.png)
Figure 1:Forecasts from an MLP and an ARMA without preprocessing\. \(a\) Stationary AR\(1\): both models track the series well\. \(b\) Trend nonstationarity: the rising level leads forecasts to lag the mean learned in training\. \(c\) Variance nonstationarity: the mean is captured but larger fluctuations inflate absolute errors\. \(d\) Random walk: persistent level changes cause drift and error accumulation\. \(e\) Seasonality: without seasonal modeling, forecasts revert to the global mean and miss cyclic fluctuations\. \(f\) Multi: multiple interacting forms of nonstationarity amplify drift and mismatch, causing the largest forecast degradation\.Despite the importance of preprocessing, many forecasting benchmarks either report preprocessing only partially or restrict it to minimal transformations such as scaling\([Shao et al\., 2024](https://arxiv.org/html/2610.09096#bib.bib4);[Aksu et al\., 2024](https://arxiv.org/html/2610.09096#bib.bib5);[Godahewa et al\., 2021](https://arxiv.org/html/2610.09096#bib.bib2);[Qiu et al\., 2024](https://arxiv.org/html/2610.09096#bib.bib3);[Li et al\., 2025](https://arxiv.org/html/2610.09096#bib.bib6)\)\. Transformations explicitly designed to address nonstationarity are rarely treated as systematic benchmark dimensions\. As summarized in Table[1](https://arxiv.org/html/2610.09096#S1.T1), commonly used benchmarks cover a broad range of models and datasets, but they generally do not evaluate forecasting algorithms under a controlled set of nonstationarity preprocessing pipelines\.

Table 1:Benchmark characteristics\.X= Yes; Blank = No\. More in Appendix[B](https://arxiv.org/html/2610.09096#A2)\.BenchmarkStatisticalModelsMachineLearningModelsTransformer\-basedModelsTime SeriesRepresentationScalingPreprocessingNonstationarityPipelineMonash\([Godahewa et al\., 2021](https://arxiv.org/html/2610.09096#bib.bib2)\)XXXBasicTS\+\([Shao et al\., 2024](https://arxiv.org/html/2610.09096#bib.bib4)\)XXXXTFB\([Qiu et al\., 2024](https://arxiv.org/html/2610.09096#bib.bib3)\)XXXXXGIFT\-EVAL\([Aksu et al\., 2024](https://arxiv.org/html/2610.09096#bib.bib5)\)XXXXXTSFM\-Bench\([Li et al\., 2025](https://arxiv.org/html/2610.09096#bib.bib6)\)XXXXXOursXXXXXX

This omission matters because preprocessing capacity is not distributed equally across forecasting methods\. Some models include transformations that address nonstationarity as part of the model itself\. For example, ARIMA incorporates differencing\([Box et al\., 2015](https://arxiv.org/html/2610.09096#bib.bib20)\), while recent neural approaches may include normalization mechanisms such as RevIN\([Kim et al\., 2021](https://arxiv.org/html/2610.09096#bib.bib9)\), as used in PatchTST\([Nie et al\., 2023](https://arxiv.org/html/2610.09096#bib.bib22)\)\. We refer to such methods asInternalizedPreprocessing Models \(IP\-Models\), because part of the preprocessing burden is embedded within the model rather than applied externally\.

When a benchmark applies only minimal external preprocessing, IP\-Models may benefit from transformations unavailable to models without such built\-in mechanisms\. For example, recent studies have shown that RevIN can substantially influence the performance of state\-of\-the\-art time series forecasting models\([Zhang et al\., 2024](https://arxiv.org/html/2610.09096#bib.bib24);[Fu and Yang, 2025](https://arxiv.org/html/2610.09096#bib.bib31)\)\. As a result, benchmark outcomes may reflect not only architectural merit, but also unequal access to preprocessing capacity\.

We refer to this phenomenon asstructural preprocessing bias: a benchmark condition in which some models have access to preprocessing capabilities, either internally or externally, while others are evaluated under less favorable data conditions\. This does not invalidate existing benchmarks\. Rather, it limits the extent to which model\-centric leaderboards can be interpreted as measuring forecasting architecture alone\.Without a controlled treatment of preprocessing, it remains unclear whether observed performance differences arise from the forecasting model, from the preprocessing implicitly available to that model, or from the interaction between the two\.

To address this gap, we propose a preprocessing\-aware benchmarking framework for time series forecasting that decouples architectural merit from data transformation effects\. The goal is to evaluate not only which models perform best under a fixed conventional pipeline, but also how different preprocessing strategies interact with different forecasting algorithms\. In particular, we study how optimal and reversible preprocessing pipelines designed to handle nonstationarity affect the absolute performance and relative ranking of statistical, machine learning, and transformer\-based forecasting methods\.

The benchmark is conducted on a curated subset of the M4 competition dataset, comprising around 29,000 time series from multiple domains and frequencies\([Makridakis et al\., 2020](https://arxiv.org/html/2610.09096#bib.bib1)\)\. We evaluate 11 forecasting algorithms spanning statistical, machine learning, and transformer\-based approaches, each combined with 16 reversible preprocessing pipelines\.

The main contributions of this work are:

- •We propose a preprocessing\-aware benchmark for time series forecasting that systematically combines diverse forecasting algorithms with diverse, reversible preprocessing pipelines for handling nonstationarity\.
- •We analyze model sensitivity to preprocessing across statistical, machine learning, and transformer\-based methods, showing that preprocessing can substantially alter both absolute performance and relative model rankings\.
- •We release the complete collection of 5\.1 million experimental results as a metadataset, enabling further analysis of the relationship between time series characteristics, preprocessing strategies, and forecasting performance\.

## 2Time Series Preliminaries

A time series is an ordered collection of observations indexed by time,X=\[x1,x2,…,xn\]X=\[x\_\{1\},x\_\{2\},…,x\_\{n\}\], usually recorded at regular intervals\. The data may reflect continuous phenomena or discrete counts\. For example, daily temperature is often treated as continuous, while the number of daily hotel visitors is discrete\. Each value is time\-dependent, meaning that its magnitude can be influenced by the time it was measured and by prior observations\.

2\.1 Time Series Characteristics\.A time series can be described by a set of features that summarize the temporal structure of the time series\. Those descriptors give us a broader view to compare structures across datasets\. Such representations are used in many fields, such as forecasting method selection\([Ding et al\., 2018](https://arxiv.org/html/2610.09096#bib.bib16)\), meta\-learning\([Talagala et al\., 2023](https://arxiv.org/html/2610.09096#bib.bib17);[Montero\-Manso et al\., 2018](https://arxiv.org/html/2610.09096#bib.bib7)\), classification and clustering\([Ismail Fawaz et al\., 2019](https://arxiv.org/html/2610.09096#bib.bib18)\), anomaly detection\([Blázquez\-García et al\., 2021](https://arxiv.org/html/2610.09096#bib.bib19)\), etc\. In this research, we describe key time series descriptors, including trend, seasonality, and stationarity\([Box et al\., 2015](https://arxiv.org/html/2610.09096#bib.bib20)\)\. The features used in this study are listed and described in Appendix[C](https://arxiv.org/html/2610.09096#A3)\.

2\.2 Time Series Preprocessing\.Proper preprocessing is essential in time series forecasting because many traditional and machine learning estimators rely on specific statistical assumptions about their inputs\([Box et al\., 2015](https://arxiv.org/html/2610.09096#bib.bib20)\)\. When these assumptions are violated, parameter estimates, diagnostics, and predictive performance can degrade\([Hyndman and Athanasopoulos, 2018](https://arxiv.org/html/2610.09096#bib.bib21)\)\. A primary objective is often achieving weak stationarity; thus, we apply transformations to remove or mitigate nonstationary components\. For instance, as illustrated in Figure[1](https://arxiv.org/html/2610.09096#S1.F1)\(d\), a series exhibiting a unit root can be transformed via differencing to yield a series that is closer to stationarity \(a\), which can improve the performance of models that assume such properties\.

Synthesizing standard practices in the field\([Hyndman and Athanasopoulos, 2018](https://arxiv.org/html/2610.09096#bib.bib21)\), we categorize these transformations into \(i\) variance\-stabilizing transforms, \(ii\) difference\-based unit root removal, and \(iii\) scaling\. Within the scope of this study, the selected transformations are invertible, allowing forecasts to be mapped back to the original scale\. Appendix[D](https://arxiv.org/html/2610.09096#A4)contains a detailed description of the techniques used in this work\.

Internalized\-Preprocessing Models\.We define anIP\-Modelas a composite architecture that maps an input sequences⊂Xs\\subset Xto a forecasty^\\hat\{y\}by embedding a preprocessing pipelineppdirectly within the model’s computational flow\. Formally:

y^=p−1​\(F⁡\(p⁡\(s\)\)\)\\hat\{y\}=p^\{\-1\}\(F\(p\(s\)\)\)\(1\)wherepprepresents a modular transformation \(such as RevIN\([Kim et al\., 2021](https://arxiv.org/html/2610.09096#bib.bib9)\), differencing, or decomposition\) designed to transform data, specifically nonstationarity, prior to the learning phase of the core forecasting algorithmFF\. This distinguishes IP\-Models from standard architectures whereppis either absent or applied as a disjoint, external step\. This differs from "structural features" \(like patching or convolutions\), which define the architecture’s view of the data rather than its statistical state\.

## 3Preprocessing\-Aware Time Series Benchmark

To analyze the impact of preprocessing on time series forecasting, we benchmark multiple forecasting algorithms under diverse preprocessing pipelines\. All metadata and results are saved in aPreprocessing\-AwareTime SeriesMetadataset \(PATM\), shown in Figure[2](https://arxiv.org/html/2610.09096#S3.F2)\.

![Refer to caption](https://arxiv.org/html/2610.09096v1/figures/patm.png)
Figure 2:Preprocessing\-Aware Time Series Benchmark framework and Metadataset\.To ensure the benchmark captures performance across varied data regimes, we establish an experimental corpus𝔻=\{D1,D2,…,Dℓ\}\\mathbb\{D\}=\\\{D\_\{1\},D\_\{2\},\\dots,D\_\{\\ell\}\\\}\. We contextualize each datasetDiD\_\{i\}by extracting a vector of descriptive features𝐟i=\(fi1,fi2,…,fiz\)\\mathbf\{f\}\_\{i\}=\(f\_\{i\}^\{1\},f\_\{i\}^\{2\},\\dots,f\_\{i\}^\{z\}\)\. These descriptors represent the structural properties of the series, allowing us to analyze how specific data characteristics interact with preprocessing choices to influence model success\.

A core contribution of this benchmark is the formalization of the preprocessing search space\. We define four critical categories of transformations: \(1\)𝕍\\mathbb\{V\}: variance\-stabilizing transformation techniques \(vi∈𝕍v\_\{i\}\\in\\mathbb\{V\}\); \(2\)𝕌\\mathbb\{U\}: unit\-root removal techniques \(ui∈𝕌u\_\{i\}\\in\\mathbb\{U\}\); \(3\)𝕊\\mathbb\{S\}: seasonality removal techniques \(si∈𝕊s\_\{i\}\\in\\mathbb\{S\}\); \(4\)ℚ\\mathbb\{Q\}: scaling techniques \(qi∈ℚq\_\{i\}\\in\\mathbb\{Q\}\)\.

By considering the Cartesian product of these techniques, we define a pipeline spaceℙ=𝕍×𝕌×𝕊×ℚ\\mathbb\{P\}=\\mathbb\{V\}\\times\\mathbb\{U\}\\times\\mathbb\{S\}\\times\\mathbb\{Q\}, with\|ℙ\|:=m\|\\mathbb\{P\}\|:=m\. Each datasetDiD\_\{i\}is processed through every pipelinepj∈ℙp\_\{j\}\\in\\mathbb\{P\}to create a variantDi\(j\)=pj​\(Di\)D\_\{i\}^\{\(j\)\}=p\_\{j\}\(D\_\{i\}\)\. This exhaustive design ensures full transparency and reproducibility while strictly preventing data leakage by fitting transformation parameters solely on training windows\.

We evaluate a broad spectrum of forecasting algorithms𝔽=\{F1,F2,…,Fn\}\\mathbb\{F\}=\\\{F\_\{1\},F\_\{2\},\\dots,F\_\{n\}\\\}, spanning statistical methods, classical machine learning, deep learning, and transformer\-based architectures\. For every preprocessed variantDi\(j\)D\_\{i\}^\{\(j\)\}, we execute a standardized training and inference protocol\. Instead of accuracy\-only leaderboards, we collect a multi\-objective set of results for each experiment\(i,j,k\)\(i,j,k\): performance metrics𝐫i,j,k∈ℝr\\mathbf\{r\}\_\{i,j,k\}\\in\\mathbb\{R\}^\{r\}, cost metrics𝐞i,j,k∈ℝe\\mathbf\{e\}\_\{i,j,k\}\\in\\mathbb\{R\}^\{e\}, and configuration record𝐡i,j,k∈ℝh\\mathbf\{h\}\_\{i,j,k\}\\in\\mathbb\{R\}^\{h\}that contains model identity, and random seeds\.

This benchmarking protocol enables a granular analysis of where preprocessing exerts the most significant impact—be it across dataset families, types of nonstationarity, or model architectures\. We formalize the resulting metadataset generated by this extensive benchmark as the set of tuples:

P​A​T​M⋆=\{\(𝐟𝐢,pj,Fk,𝐫i,j,k,𝐞i,j,k,𝐡i,j,k\)\|i∈\{1,…,ℓ\},j∈\{1,…,m\},k∈\{1,…,n\}\}\.PATM^\{\\star\}=\\left\\\{\(\\mathbf\{f\_\{i\}\},p\_\{j\},F\_\{k\},\\mathbf\{r\}\_\{i,j,k\},\\mathbf\{e\}\_\{i,j,k\},\\mathbf\{h\}\_\{i,j,k\}\)\\;\\middle\|\\;\\begin\{aligned\} &i\\in\\\{1,\\dots,\\ell\\\},\\\\ &j\\in\\\{1,\\dots,m\\\},\\\\ &k\\in\\\{1,\\dots,n\\\}\\end\{aligned\}\\right\\\}\.\(2\)

## 4Experimental Protocol

Hardware\.All experiments were run on a dedicated compute server\. Detailed hardware and software specifications are reported in Appendix[E](https://arxiv.org/html/2610.09096#A5)\.

Datasets\.The evaluation focuses on univariate time series in order to isolate the effect of preprocessing\. Multivariate settings introduce cross\-channel interactions that can obscure the individual contribution of preprocessing to forecasting accuracy, as performance gains may arise from implicit information sharing rather than the transformations themselves\. Moreover, recent work\([Nie et al\., 2023](https://arxiv.org/html/2610.09096#bib.bib22)\)shows that modeling each channel independently can achieve competitive or even superior performance compared to approaches that explicitly model inter\-variable dependencies\. The M4 dataset\([Makridakis et al\., 2020](https://arxiv.org/html/2610.09096#bib.bib1)\)provides an appropriate benchmark for this purpose, as it contains real\-world time series from diverse application domains \(e\.g\., Demographic, Macro, Industry, Finance\)\([Godahewa et al\., 2021](https://arxiv.org/html/2610.09096#bib.bib2)\)and various temporal granularities\. We utilize the quarterly, weekly, daily, and hourly subsets but exclude the yearly data\. Yearly series are omitted because they lack a seasonal period, rendering seasonal differencing inapplicable and yielding no useful results for the analysis of seasonal transformations\. The main characteristics of the dataset are shown in Table[2](https://arxiv.org/html/2610.09096#S4.T2)\. Prior analyses\([Kang et al\., 2020](https://arxiv.org/html/2610.09096#bib.bib25);[Talagala et al\., 2022](https://arxiv.org/html/2610.09096#bib.bib26)\)have shown that the M4 dataset exhibits broad variability in trend behavior, seasonal patterns, autocorrelation profiles, and noise characteristics, which makes it suitable for assessing general forecasting performance across heterogeneous conditions\. We adhere to the standard forecasting horizons defined in the M4 competition for each temporal granularity\.

Table 2:Main characteristics of the M4 datasets used in this study\. Lag and horizon are reported in the number of time steps\.DatasetFreq\.\# SeriesAvg\. Length\# Obs\.LagHorizonM4 QuarterlyQuarterly24,0001002,406,10848M4 WeeklyWeekly3591,035371,5795213M4 DailyDaily4,2272,37110,023,836714M4 HourlyHourly414902373,3722448

Pipelines\.We conduct a grid evaluation over the pipeline spaceℙ\\mathbb\{P\}\. Operations are applied in a fixed sequence: variance\-stabilization \(𝕍\\mathbb\{V\}\), seasonal removal \(𝕊\\mathbb\{S\}\), unit\-root removal \(𝕌\\mathbb\{U\}\), and scaling \(ℚ\\mathbb\{Q\}\)\. We consider𝕍∈\{none,boxcox\}\\mathbb\{V\}\\in\\\{\\text\{none\},\\text\{boxcox\}\\\},𝕌∈\{none,diff\}\\mathbb\{U\}\\in\\\{\\text\{none\},\\text\{diff\}\\\},𝕊∈\{none,sdiff\}\\mathbb\{S\}\\in\\\{\\text\{none\},\\text\{sdiff\}\\\}, andℚ∈\{none,z\-score\}\\mathbb\{Q\}\\in\\\{\\text\{none\},\\text\{z\-score\}\\\}, resulting in 16 combinations\. This sequence follows established frameworks\([Hyndman and Athanasopoulos, 2018](https://arxiv.org/html/2610.09096#bib.bib21)\), ensuring variance is stabilized prior to differencing operations that can produce non\-positive values\. The setup prioritizes established, interpretable methods to isolate the systematic role of preprocessing without the interference of learned feature extractions\.

Forecasting Algorithms\.The selected model set includesETS,ARIMA, andThetaas representatives of classical statistical forecasting\.Linear RegressionandXGBoostserve as machine learning baselines\.MLP,N\-BEATS, andTimesNetrepresent deep learning architectures\.PatchTSTandInformerare also deep learning architectures, but are included as transformer\-based models designed for high\-capacity sequence modeling\. Additionally, we evaluateChronos2\-Synth\([Ansari et al\., 2025](https://arxiv.org/html/2610.09096#bib.bib32)\), a time series foundation model pre\-trained exclusively on synthetic data\. Foundation models represent a promising paradigm in forecasting with strong zero\-shot generalization capabilities, making the analysis of their preprocessing sensitivity critical for future development\. We specifically rely on a synthetically trained model to rigorously prevent data leakage\. Since evaluating models trained on real\-world corpora poses a significant risk that the M4 benchmark data was included in their pre\-training set\([Meyer et al\., 2026](https://arxiv.org/html/2610.09096#bib.bib36)\), synthetic pre\-training naturally avoids this overlap\. This approach justifies the exclusion of other real\-data foundation models and ensures that any observed performance variations reflect the model’s true structural priors rather than memorization\. Based on our proposed taxonomy, we classifyARIMA,ETS,Theta,TimesNet,PatchTST, andChronos2\-Synthas IP\-Models\. The total number of experiments is1111models×\\times1616pipelines×\\timesapproximately29,00029\{,\}000series≈5\.1×106\\approx 5\.1\\times 10^\{6\}experiments\. To strictly isolate the performance impact of preprocessing from model capacity, all hyperparameters and lag window lengths were adopted directly from established benchmark practices following the specifications documented by[Godahewa et al\. \(2021\)](https://arxiv.org/html/2610.09096#bib.bib2)\. Further details regarding this methodology and its trade\-offs are provided in Appendix[F](https://arxiv.org/html/2610.09096#A6)\.

Evaluation Metrics\.We record five performance metrics for every experiment: MSE, RMSE, MAE, sMAPE, and MASE\. To maintain conciseness in our primary analysis and visualizations, we report the MASE as the primary metric\. We prioritize MASE because it is strictly scale\-independent, a necessity given that the M4 dataset aggregates series from disparate domains with different magnitudes\.

## 5Results

Table[3](https://arxiv.org/html/2610.09096#S5.T3)reports forecasting performance when a single preprocessing pipeline is selected and applied uniformly to the entire dataset\. This setting reflects the standard design of many forecasting benchmarks, where a fixed and relatively simple preprocessing strategy, such as no transformation \(XX\) or standard scaling \(QQ\), is used for all models and all series333Pipelines are composed of:X\(Baseline/None\),V\(Boxcox transformation\),U\(First\-order differencing\),S\(Seasonal differencing\), andQ\(Standard scaling\)\.\. While this protocol simplifies evaluation, it can introduce severe mismatches between the chosen pipeline and the statistical properties of individual series\. For instance, when combiningVV,UU, andSS\(such as in the VUS pipeline\), error metrics often explode across several models\. This occurs because the benchmark includes the full breadth of the M4 dataset, including non\-seasonal series, without prior filtering\. Applying seasonal and first\-order differencing in such cases acts as a noise amplifier\. When models produce erratic forecasts on these overly\-differenced series, the inverse Box\-Cox transformation exponentially amplifies these errors when returning the predictions to the original scale\.

Under this evaluation protocol, IP\-Models obtain the strongest overall results\. In particular, when no preprocessing is applied, IP\-Models achieve lower MASE than all non\-IP\-Models, and this advantage remains under standard scaling\. This result supports the presence ofstructural preprocessing bias\. Because IP\-Models already include mechanisms that stabilize or adapt the input series, they are less dependent on the externally selected preprocessing pipeline\. As a result, they remain competitive even when the benchmark uses a minimal or generic transformation\. In contrast, non\-IP\-Models show stronger dependence on the chosen pipeline\. For example, LR, XGBoost, and Informer improve substantially under differencing \(UU\)\. This suggests that the performance of these models is disproportionately sensitive to whether the external preprocessing pipeline matches the series’ statistical structure\.

The best fixed\-pipeline results further illustrate this distinction\. The best IP\-Model performance remains concentrated around simple or internally compatible pipelines, whereas the best non\-IP\-Model results require more specific preprocessing choices\. Therefore, when a benchmark evaluates all series under a single global pipeline, it tends to favor models that are resilient to preprocessing misspecification\. This raises an important question:are IP\-Models intrinsically better forecasters, or are they favored by benchmark protocols that use a single global preprocessing choice?

Table 3:Forecasting performance \(MASE\) across preprocessing pipelines and models\. Best per model in bold\. Columns in grey are IP\-Models\. Pipelines are composed of:X\(None\),V\(Boxcox transformation\),U\(First\-order differencing\),S\(Seasonal differencing\), andQ\(Standard scaling\)\.PipelineARIMAETSTHETALRXGBstMLPNBTSTNetPTSTInformerChronosX2\.352\.252\.222\.872\.7531\.884\.652\.652\.77106\.752\.29V3\.182\.382\.363\.752\.614\.274\.782\.452\.4846\.122\.56U2\.232\.402\.602\.272\.343\.105\.913\.083\.163\.122\.09S2\.383\.193\.192\.712\.494\.065\.783\.103\.424\.452\.46Q2\.302\.182\.222\.873\.714\.864\.862\.542\.665\.512\.29VU2\.232\.452\.842\.452\.182\.871\.48​e241\.48e^\{24\}3\.353\.473\.212\.17VS2\.813\.853\.832\.35​e42\.35e^\{4\}2\.342\.812\.723\.203\.222\.742\.66VQ2\.282\.382\.383\.753\.785\.472\.662\.542\.625\.312\.35US2\.443\.814\.473\.132\.863\.319\.826\.606\.536\.453\.28UQ2\.202\.342\.602\.272\.162\.215\.803\.083\.042\.252\.09SQ2\.393\.133\.192\.712\.362\.582\.533\.033\.022\.492\.46VUS2\.5727\.022\.99​e42\.99e^\{4\}1\.38​e371\.38e^\{37\}2\.953\.804\.97​e354\.97e^\{35\}7\.19​e47\.19e^\{4\}2\.42​e52\.42e^\{5\}3\.705\.27VUQ2\.332\.452\.852\.452\.362\.551\.38​e241\.38e^\{24\}3\.223\.542\.452\.17VSQ2\.913\.593\.832\.35​e42\.35e^\{4\}2\.542\.743\.733\.243\.142\.752\.66USQ2\.723\.654\.473\.132\.973\.033\.466\.346\.473\.173\.28VUSQ3\.2227\.013\.01​e43\.01e^\{4\}1\.38​e371\.38e^\{37\}3\.273\.135\.19​e355\.19e^\{35\}8\.96​e68\.96e^\{6\}1\.56​e51\.56e^\{5\}3\.855\.28

Per\-series preprocessing significantly impacts model performance\.Figure[3](https://arxiv.org/html/2610.09096#S5.F3)compares each model under four preprocessing settings:*No Pipeline*, the single*Best Global*pipeline, the*Worst*global pipeline, and an*Oracle*configuration in which the best preprocessing pipeline is selected separately for each time series\. The comparison shows two distinct behaviors\. First, IP\-Models exhibit only small differences between theNo PipelineandGlobal Bestsettings, reinforcing that these models are relatively robust to preprocessing misspecification and can perform well even when little or no external preprocessing is applied\. In contrast, most non\-IP\-Models already improve when moving from no preprocessing to the best global pipeline, indicating that evaluating them on raw data places them at a disadvantage\.

![Refer to caption](https://arxiv.org/html/2610.09096v1/figures/fourbars.png)Figure 3:Barplot MASE of best and oracle pipelines\. Lower loss values mean better results\.TheOraclesetting further amplifies this difference\. Since the oracle selects the best pipeline per series, all models improve by definition\. However, the magnitude of improvement remains much larger for non\-IP\-Models\. While IP\-Models show substantial oracle gains against the no pipeline baseline \(ranging from approximately 35% to 55%\), the improvement is even more dramatic for non\-IP\-Models\. Specifically, four out of the five non\-IP\-Models improve by more than 50%, with models like MLP and Informer improving by over 75%\. In some cases, this allows non\-IP\-Models to close the performance gap with IP\-Models\.These results suggest that the strong relative standing of IP\-Models under fixed benchmark pipelines is partly explained by their robustness to generic preprocessing, whereas non\-IP\-Models benefit more strongly when preprocessing is adapted to the statistical properties of each series\.Therefore, neglecting per\-series preprocessing can create an unfair comparison by systematically underestimating models that rely more heavily on external data transformations\. Additional results are provided in Appendix[I\.2](https://arxiv.org/html/2610.09096#A9.SS2)\.

Preprocessing changes model rankings\.Figure[4](https://arxiv.org/html/2610.09096#S5.F4)analyzes preprocessing preferences through an intra\-model ranking, where each model is compared only against its own performance under different pipelines\. This view reveals two distinct patterns\. IP\-Models generally obtain their best ranks under simple pipelines such asXX,VV,QQ, andV​QVQ, while heavily stacked transformations such asV​U​SVUS,U​S​QUSQ, andV​U​S​QVUSQtend to perform poorly\. This reinforces that these models are relatively robust to minimal preprocessing and do not usually require aggressive external transformations\.

![Refer to caption](https://arxiv.org/html/2610.09096v1/figures/rankmap.png)Figure 4:Intra\-model average rank of each preprocessing pipeline\. Each model is ranked only against itself across pipelines; lower ranks indicate better preprocessing choices for that model\.
OracleXVUSQARIMA5\.94±\\pm3\.284\.99±\\pm2\.545\.15±\\pm2\.805\.30±\\pm3\.034\.99±\\pm3\.154\.93±\\pm2\.65ETS6\.70±\\pm3\.004\.61±\\pm2\.664\.73±\\pm2\.665\.25±\\pm2\.766\.18±\\pm2\.894\.51±\\pm2\.81THETA6\.76±\\pm3\.084\.73±\\pm2\.524\.97±\\pm2\.535\.79±\\pm2\.986\.51±\\pm3\.004\.74±\\pm3\.02LR6\.87±\\pm3\.345\.54±\\pm3\.155\.66±\\pm3\.155\.23±\\pm3\.015\.38±\\pm3\.175\.61±\\pm3\.38XGBoost5\.48±\\pm2\.895\.47±\\pm2\.995\.47±\\pm2\.725\.28±\\pm2\.615\.06±\\pm2\.686\.38±\\pm2\.49MLP4\.88±\\pm2\.727\.34±\\pm2\.976\.92±\\pm3\.466\.17±\\pm3\.006\.65±\\pm3\.477\.58±\\pm2\.89N\-BEATS5\.39±\\pm3\.095\.63±\\pm2\.965\.93±\\pm3\.068\.53±\\pm3\.406\.53±\\pm3\.077\.65±\\pm3\.41TimesNet6\.25±\\pm3\.276\.05±\\pm2\.645\.59±\\pm2\.536\.68±\\pm3\.266\.14±\\pm3\.105\.74±\\pm2\.59PatchTST6\.15±\\pm3\.236\.40±\\pm2\.785\.71±\\pm2\.456\.87±\\pm3\.276\.87±\\pm3\.375\.82±\\pm2\.47Informer5\.23±\\pm2\.9210\.35±\\pm2\.0110\.40±\\pm1\.986\.17±\\pm2\.966\.61±\\pm3\.218\.18±\\pm3\.16Chronos2Synth6\.34±\\pm3\.184\.90±\\pm2\.785\.37±\\pm2\.974\.68±\\pm2\.445\.01±\\pm2\.684\.85±\\pm2\.99

Table 4:Inter\-model mean rank \(±\\pmstd\) under selected preprocessing configurations\. Lower ranks indicate better relative performance\. Grey rows indicate IP\-Models\. Bold values indicate the three best\-ranked models within each column, including ties\.

Non\-IP\-Models show a more heterogeneous profile\. Their preferred pipelines vary substantially across architectures\. For example,UUis beneficial for LR but extremely harmful for N\-BEATS\. Nevertheless, most non\-IP\-Models benefit from pipelines involving first\-order differencing \(UU\), suggesting that external stationarity\-inducing transformations play a larger role for models without internalized preprocessing mechanisms\. Thus, the heatmap shows that preprocessing is not only important in magnitude, but also model\-dependent in direction\. A more detailed, per\-model view is shown in Appendix[I\.3](https://arxiv.org/html/2610.09096#A9.SS3)\.

Table[4](https://arxiv.org/html/2610.09096#S5.T4)shifts from this intra\-model view to an inter\-model ranking, where models are compared against each other under the same preprocessing configuration\. Under the commonly usedQQpipeline\([Qiu et al\., 2024](https://arxiv.org/html/2610.09096#bib.bib3);[Godahewa et al\., 2021](https://arxiv.org/html/2610.09096#bib.bib2);[Shao et al\., 2024](https://arxiv.org/html/2610.09096#bib.bib4);[Aksu et al\., 2024](https://arxiv.org/html/2610.09096#bib.bib5);[Li et al\., 2025](https://arxiv.org/html/2610.09096#bib.bib6)\), the best ranks are dominated by IP\-Models\. However, under the oracle setting, the relative positioning shifts favorably for several non\-IP\-Models\. Although this comparison should not be interpreted as a fully optimized leaderboard, since no model\-specific hyperparameter search is performed, it shows that relative model standings can change substantially once preprocessing is selected per series\. This supports our central claim: fixed preprocessing protocols can favor models that are robust to generic pipelines, while underestimating models whose performance depends more strongly on appropriate external transformations\.

Preprocessing Preferences Depend on Model and Series Properties\.Table[5](https://arxiv.org/html/2610.09096#S5.T5)reports the single preprocessing pipeline that achieved the best overall MASE for each model across different data characteristics\. This analysis demonstrates that preprocessing effectiveness is not only model\-dependent but also strongly conditioned by the statistical properties of the input series\. For a more granular visualization showing the frequency of pipelines appearing in the Top\-3, see Appendix[I\.1](https://arxiv.org/html/2610.09096#A9.SS1)\.

Table 5:Best performing preprocessing pipelines \(MASE\) for each model under different statistical properties\. IP\-Models are highlighted in gray\.TrendSeasonalityStationarityShiftingEntropyModelHighLowHighLowStat\.Non\-Stat\.HighLowHighLowARIMAVUQVSVUQVUQVUQVUQVUQVUQVQVUQETSXQQXVVQQVQVVTHETAXXXXXXXVQQQLRVUVVUVUUQVUVUQVVUQXGBoostVUQVQVSQVUQSQVUQVUQVUQVQVUQMLPVUQVSQVSQUQVUSQVUQVUQQVQUSQN\-BEATSVUQSQSQUQSQVUQSQVUQQSQTimesNetVQQQVQQVQVQVQVQQPatchTSTVQVQSQVQVQVQVQQVQVInformerVUQSQUSQVUUQVUQVUQVQVQVUQChronos2SynthVUQVQQVUQQVUQQXQVU

The clearest patterns emerge from the trend and non\-stationarity splits\. When trend strength is low or the series is stationary, most models perform best with simple pipelines such asXX,VV,QQ, andV​QVQ\. When trend strength is high or the data is highly non\-stationary, however, non\-IP\-Models shift toward pipelines involving first\-order or seasonal differencing\. For example, XGBoost, MLP, N\-BEATS, and Informer overwhelmingly favor variants likeV​U​QVUQ,U​QUQ, orU​S​QUSQunder high trend and non\-stationarity\. This behavior aligns with the classical role of differencing in removing trend\-induced drifts\. In contrast, IP\-Models like THETA, TimesNet, and PatchTST preserve much simpler preprocessing preferences across these challenging subsets, indicating that their internal mechanisms successfully reduce their dependence on heavy external transformations\. A notable exception is ARIMA, which strongly prefers the VUQ pipeline, likely because external variance stabilization and scaling help the algorithm more stably identify and fit the appropriate internal integration order\.

The stationarity and shifting splits produce results that further validate our core argument\. Because standard stationarity tests do not distinguish whether the difficulty arises primarily from trend, seasonality, or variance changes, the preferred pipelines for the non\-stationary subset are typically comprehensive transformations likeV​U​QVUQ\. These robust pipelines address multiple forms of degradation simultaneously\. This analysis shows that structural preprocessing bias emerges precisely because different forms of non\-stationarity affect model families differently, and fixing a single global pipeline will inevitably penalize models that lack internal stabilization mechanisms\.

Cost accounting reveals efficiency trade\-offs that preprocessing can optimize\.Figure[5](https://arxiv.org/html/2610.09096#S5.F5)exposes the trade\-off between predictive accuracy, training time, and peak GPU memory usage\. To calculate the computational impact fairly and independently of dataset benchmark structure, we evaluate models by training them locally on each individual series\. Deep learning models often exhibit substantially longer training times and higher memory footprints\. However, when optimal preprocessing is applied, classical models like LR and THETA, as well as simpler machine learning models, achieve highly competitive performance with a fraction of the computational cost\. Importantly, applying these preprocessing pipelines provides a significant performance boost with virtually no practical increase in training time\. For a broader perspective on cost when machine learning models are trained globally across multiple series simultaneously, refer to Appendix[I\.4](https://arxiv.org/html/2610.09096#A9.SS4)\. Note that Chronos2Synth is excluded from this figure because it is a zero\-shot model and requires no training\.

![Refer to caption](https://arxiv.org/html/2610.09096v1/figures/gpu_local2.png)Figure 5:Mean MASE vs\. mean training time for local models\. Marker size indicates peak GPU memory \(baselined at 250MB for CPU\-only models\)\.
## 6Conclusion

This paper introduced a preprocessing\-aware benchmark for time series forecasting, showing that model performance and rankings are strongly shaped by the preprocessing pipeline used during evaluation\. Across statistical, machine learning, and transformer\-based models, we found that fixed global pipelines favor models with internalized preprocessing mechanisms, while models without such mechanisms benefit substantially more when preprocessing is selected per series\. We refer to this effect asstructural preprocessing bias: an evaluation artifact in which benchmark outcomes reflect unequal access to preprocessing capacity in addition to architectural merit\. Our results show that preprocessing preferences depend on both model class and series properties, with trend and seasonality inducing clear shifts toward differencing\-based pipelines for non\-IP\-Models\. These findings suggest that forecasting benchmarks should treat preprocessing as an explicit evaluation dimension rather than a secondary implementation detail\. To support further work, we release the PATM metadataset as a resource for studying preprocessing sensitivity and developing adaptive preprocessing selection methods\.

### AI use statement

\(This section isrequiredand does not count toward the page limit\.\)

In this work, we used generative AI tools to assist in editing the research paper to improve readability, format and create tables, and edit software code by polishing, commenting, and refactoring it\. We have not used generative AI tools for generating synthetic datasets, developing theoretical models or conceptual frameworks, formulating mathematical claims, proving mathematical claims, proposing or refining hypotheses, designing or providing feedback on research methodology or experiments, interpreting results, or any other tasks with required disclosure\. We have reviewed all AI\-assisted work\. AI\-generated text and tables were manually verified for accuracy and consistency with our findings\. LLM\-generated and refactored code was thoroughly reviewed and tested for correctness by the authors\. We take responsibility for the final content of this work, including text, claims, and artifacts produced with the aid of generative AI\.

### Ethics statement

\(This section isrecommendedand does not count toward the page limit\.\)

This research does not involve human subjects, nor does it rely on sensitive or proprietary data\. We rely exclusively on publicly available datasets that have been anonymized and widely adopted in the forecasting literature\. We believe there are no significant ethical concerns, potential conflicts of interest, privacy issues, or risks of harm associated with this work and its applications\.

### Reproducibility statement

\(This section isrecommendedand does not count toward the page limit\.\)

To ensure the full reproducibility of our benchmark and findings, we provide comprehensive details and open\-source materials\. We outline our experimental protocol, including dataset characteristics, model selections, and evaluation procedures, in Section 4\. Detailed descriptions of the extracted time series features and the preprocessing transformations are provided in Appendix[C](https://arxiv.org/html/2610.09096#A3)and Appendix[D](https://arxiv.org/html/2610.09096#A4)\. Hardware specifications and complete model hyperparameters, including training configurations and lookback window settings, are documented in Appendix[E](https://arxiv.org/html/2610.09096#A5)and Appendix[F](https://arxiv.org/html/2610.09096#A6)\. Mathematical definitions for all evaluation metrics are listed in Appendix[H](https://arxiv.org/html/2610.09096#A8)\. Finally, we provide anonymized links to our source code and the complete generated metadataset in the abstract\. This allows researchers to reproduce all experiments, figures, and tables presented in this work\.

## References

- T\. Aksu, G\. Woo, J\. Liu, X\. Liu, C\. Liu, S\. Savarese, C\. Xiong, and D\. SahooGIFT\-eval: a benchmark for general time series forecasting model evaluation\.External Links:2410\.10393,[Link](https://arxiv.org/abs/2410.10393)Cited by:[Appendix B](https://arxiv.org/html/2610.09096#A2.p1.1),[§F\.1](https://arxiv.org/html/2610.09096#A6.SS1.p1.1),[Table 1](https://arxiv.org/html/2610.09096#S1.T1.4.1.1.1.5.1),[§1](https://arxiv.org/html/2610.09096#S1.p4.1),[§5](https://arxiv.org/html/2610.09096#S5.p8.1)\.
- Ansariet al\.\(2025\)A\. F\. Ansari, O\. Shchur, J\. Küken, A\. Auer, B\. Han, P\. Mercado, S\. S\. Rangapuram, H\. Shen, L\. Stella, X\. Zhang, M\. Goswami, S\. Kapoor, D\. C\. Maddix, P\. Guerron, T\. Hu, J\. Yin, N\. Erickson, P\. M\. Desai, H\. Wang, H\. Rangwala, G\. Karypis, Y\. Wang, and M\. Bohlke\-SchneiderChronos\-2: from univariate to universal forecasting\.External Links:2510\.15821,[Link](https://arxiv.org/abs/2510.15821)Cited by:[§4](https://arxiv.org/html/2610.09096#S4.p4.1)\.
- Benidiset al\.\(2022\)K\. Benidis, S\. S\. Rangapuram, V\. Flunkert, Y\. Wang, D\. Maddix, C\. Turkmen, J\. Gasthaus, M\. Bohlke\-Schneider, D\. Salinas, L\. Stella,et al\.Deep learning for time series forecasting: tutorial and literature survey\.ACM Computing Surveys55\(6\),pp\. 1–36\.Cited by:[Appendix G](https://arxiv.org/html/2610.09096#A7.p1.1)\.
- Blázquez\-Garcíaet al\.\(2021\)A\. Blázquez\-García, A\. Conde, U\. Mori, and J\. A\. LozanoA review on outlier/anomaly detection in time series data\.ACM computing surveys \(CSUR\)54\(3\),pp\. 1–33\.Cited by:[§2](https://arxiv.org/html/2610.09096#S2.p2.1)\.
- Boxet al\.\(2015\)G\. E\. P\. Box, G\. M\. Jenkins, G\. C\. Reinsel, and G\. M\. LjungTime series analysis : forecasting and control\.John Wiley & Sons,Hoboken, New Jersey\.External Links:ISBN 9781118675021Cited by:[Appendix C](https://arxiv.org/html/2610.09096#A3.p6.1),[§1](https://arxiv.org/html/2610.09096#S1.p5.1),[§2](https://arxiv.org/html/2610.09096#S2.p2.1),[§2](https://arxiv.org/html/2610.09096#S2.p3.1)\.
- Box and Cox \(1964\)G\. E\. Box and D\. R\. CoxAn analysis of transformations\.Journal of the Royal Statistical Society: Series B \(Methodological\)26\(2\),pp\. 211–243\.Cited by:[Appendix D](https://arxiv.org/html/2610.09096#A4.p2.1)\.
- Clevelandet al\.\(1990\)R\. B\. Cleveland, W\. S\. Cleveland, J\. E\. McRae, and I\. TerpenningSTL: a seasonal\-trend decomposition procedure based on loess \(with discussion\)\.Journal of Official Statistics6,pp\. 3–73\.Cited by:[Appendix C](https://arxiv.org/html/2610.09096#A3.p2.1)\.
- Debet al\.\(2017\)C\. Deb, F\. Zhang, J\. Yang, S\. E\. Lee, and K\. W\. ShahA review on time series forecasting techniques for building energy consumption\.Renewable and Sustainable Energy Reviews74,pp\. 902–924\.Cited by:[§1](https://arxiv.org/html/2610.09096#S1.p1.1)\.
- Dickey and Fuller \(1979\)D\. Dickey and W\. FullerDistribution of the estimators for autoregressive time series with a unit root\.JASA\. Journal of the American Statistical Association74,pp\.\.External Links:[Document](https://dx.doi.org/10.2307/2286348)Cited by:[Appendix C](https://arxiv.org/html/2610.09096#A3.p6.1)\.
- Dinget al\.\(2018\)J\. Ding, V\. Tarokh, and Y\. YangModel selection techniques: an overview\.IEEE Signal Processing Magazine35\(6\),pp\. 16–34\.Cited by:[§2](https://arxiv.org/html/2610.09096#S2.p2.1)\.
- Fu and Yang \(2025\)F\. Fu and Y\. YangNoise or signal? deconstructing contradictions and an adaptive remedy for reversible normalization in time series forecasting\.External Links:2510\.04667,[Link](https://arxiv.org/abs/2510.04667)Cited by:[§1](https://arxiv.org/html/2610.09096#S1.p6.1)\.
- Godahewaet al\.\(2021\)R\. Godahewa, C\. Bergmeir, G\. I\. Webb, R\. J\. Hyndman, and P\. Montero\-MansoMonash time series forecasting archive\.External Links:2105\.06643,[Link](https://arxiv.org/abs/2105.06643)Cited by:[Appendix B](https://arxiv.org/html/2610.09096#A2.p1.1),[Appendix C](https://arxiv.org/html/2610.09096#A3.p1.1),[§F\.1](https://arxiv.org/html/2610.09096#A6.SS1.p1.1),[Appendix F](https://arxiv.org/html/2610.09096#A6.p1.1),[Table 1](https://arxiv.org/html/2610.09096#S1.T1.4.1.1.1.2.1),[§1](https://arxiv.org/html/2610.09096#S1.p4.1),[§4](https://arxiv.org/html/2610.09096#S4.p2.1),[§4](https://arxiv.org/html/2610.09096#S4.p4.1),[§5](https://arxiv.org/html/2610.09096#S5.p8.1)\.
- Granger and Newbold \(2014\)C\. W\. J\. Granger and P\. NewboldForecasting economic time series\.Academic press\.Cited by:[§1](https://arxiv.org/html/2610.09096#S1.p1.1)\.
- Hyndman and Athanasopoulos \(2018\)R\. J\. Hyndman and G\. AthanasopoulosForecasting : principles and practice\.2 edition,Otexts,Heathmont, Vic\.\.External Links:ISBN 9780987507112,[Link](https://otexts.com/fpp2/)Cited by:[§1](https://arxiv.org/html/2610.09096#S1.p2.1),[§2](https://arxiv.org/html/2610.09096#S2.p3.1),[§2](https://arxiv.org/html/2610.09096#S2.p4.1),[§4](https://arxiv.org/html/2610.09096#S4.p3.1)\.
- Ismail Fawazet al\.\(2019\)H\. Ismail Fawaz, G\. Forestier, J\. Weber, L\. Idoumghar, and P\. MullerDeep learning for time series classification: a review\.Data mining and knowledge discovery33\(4\),pp\. 917–963\.Cited by:[§2](https://arxiv.org/html/2610.09096#S2.p2.1)\.
- Kanget al\.\(2020\)Y\. Kang, R\. J\. Hyndman, and F\. LiGRATIS: generating time series with diverse and controllable characteristics\.Statistical Analysis and Data Mining: The ASA Data Science Journal13\(4\),pp\. 354–376\.External Links:ISSN 1932\-1872,[Link](http://dx.doi.org/10.1002/sam.11461),[Document](https://dx.doi.org/10.1002/sam.11461)Cited by:[Appendix A](https://arxiv.org/html/2610.09096#A1.p3.1),[§4](https://arxiv.org/html/2610.09096#S4.p2.1)\.
- Kaushiket al\.\(2020\)S\. Kaushik, A\. Choudhury, P\. K\. Sheron, N\. Dasgupta, S\. Natarajan, L\. A\. Pickett, and V\. DuttAI in healthcare: time\-series forecasting using statistical, neural, and ensemble architectures\.Frontiers in big data3,pp\. 4\.Cited by:[§1](https://arxiv.org/html/2610.09096#S1.p1.1)\.
- Kimet al\.\(2021\)T\. Kim, J\. Kim, Y\. Tae, C\. Park, J\. Choi, and J\. ChooReversible instance normalization for accurate time\-series forecasting against distribution shift\.InInternational Conference on Learning Representations,External Links:[Link](https://openreview.net/forum?id=cGDAkQo1C0p)Cited by:[§1](https://arxiv.org/html/2610.09096#S1.p5.1),[§2](https://arxiv.org/html/2610.09096#S2.p5.2)\.
- Liet al\.\(2025\)Z\. Li, X\. Qiu, P\. Chen, Y\. Wang, H\. Cheng, Y\. Shu, J\. Hu, C\. Guo, A\. Zhou, C\. S\. Jensen, and B\. YangTSFM\-bench: a comprehensive and unified benchmark of foundation models for time series forecasting\.External Links:2410\.11802,[Link](https://arxiv.org/abs/2410.11802)Cited by:[Appendix B](https://arxiv.org/html/2610.09096#A2.p1.1),[§F\.1](https://arxiv.org/html/2610.09096#A6.SS1.p1.1),[Table 1](https://arxiv.org/html/2610.09096#S1.T1.4.1.1.1.6.1),[§1](https://arxiv.org/html/2610.09096#S1.p4.1),[§5](https://arxiv.org/html/2610.09096#S5.p8.1)\.
- Liuet al\.\(2023\)Y\. Liu, H\. Wu, J\. Wang, and M\. LongNon\-stationary transformers: exploring the stationarity in time series forecasting\.External Links:2205\.14415,[Link](https://arxiv.org/abs/2205.14415)Cited by:[§1](https://arxiv.org/html/2610.09096#S1.p2.1)\.
- Makridakiset al\.\(2020\)S\. Makridakis, E\. Spiliotis, and V\. AssimakopoulosThe m4 competition: 100,000 time series and 61 forecasting methods\.International Journal of Forecasting36\(1\),pp\. 54–74\.Note:M4 CompetitionExternal Links:ISSN 0169\-2070,[Document](https://dx.doi.org/https%3A//doi.org/10.1016/j.ijforecast.2019.04.014),[Link](https://www.sciencedirect.com/science/article/pii/S0169207019301128)Cited by:[Appendix B](https://arxiv.org/html/2610.09096#A2.p1.1),[§1](https://arxiv.org/html/2610.09096#S1.p9.1),[§4](https://arxiv.org/html/2610.09096#S4.p2.1)\.
- Meyeret al\.\(2026\)M\. Meyer, S\. Kaltenpoth, K\. Zalipski, and O\. MüllerRethinking evaluation in the era of time series foundation models: \(un\)known information leakage challenges\.External Links:2510\.13654,[Link](https://arxiv.org/abs/2510.13654)Cited by:[§4](https://arxiv.org/html/2610.09096#S4.p4.1)\.
- Montero\-Mansoet al\.\(2018\)P\. Montero\-Manso, G\. Athanasopoulos, R\. Hyndman, and T\. TalagalaM4metalearning\.University of A Coruña \(Spain\) and Monash University \(Australia and Sri Lanka\)\.Cited by:[§2](https://arxiv.org/html/2610.09096#S2.p2.1)\.
- Nieet al\.\(2023\)Y\. Nie, N\. H\. Nguyen, P\. Sinthong, and J\. KalagnanamA time series is worth 64 words: long\-term forecasting with transformers\.InInternational Conference on Learning Representations,Cited by:[Appendix G](https://arxiv.org/html/2610.09096#A7.p2.1),[§1](https://arxiv.org/html/2610.09096#S1.p5.1),[§4](https://arxiv.org/html/2610.09096#S4.p2.1)\.
- Pedregosaet al\.\(2011\)F\. Pedregosa, G\. Varoquaux, A\. Gramfort, V\. Michel, B\. Thirion, O\. Grisel, M\. Blondel, P\. Prettenhofer, R\. Weiss, V\. Dubourg, J\. Vanderplas, A\. Passos, D\. Cournapeau, M\. Brucher, M\. Perrot, and É\. DuchesnayScikit\-learn: machine learning in python\.Journal of Machine Learning Research12\(85\),pp\. 2825–2830\.External Links:[Link](http://jmlr.org/papers/v12/pedregosa11a.html)Cited by:[Appendix D](https://arxiv.org/html/2610.09096#A4.p13.1)\.
- Qiuet al\.\(2024\)X\. Qiu, J\. Hu, L\. Zhou, X\. Wu, J\. Du, B\. Zhang, C\. Guo, A\. Zhou, C\. S\. Jensen, Z\. Sheng, and B\. YangTFB: towards comprehensive and fair benchmarking of time series forecasting methods\.External Links:2403\.20150,[Link](https://arxiv.org/abs/2403.20150)Cited by:[Appendix B](https://arxiv.org/html/2610.09096#A2.p1.1),[§F\.1](https://arxiv.org/html/2610.09096#A6.SS1.p1.1),[Table 1](https://arxiv.org/html/2610.09096#S1.T1.4.1.1.1.4.1),[§1](https://arxiv.org/html/2610.09096#S1.p4.1),[§5](https://arxiv.org/html/2610.09096#S5.p8.1)\.
- Salleset al\.\(2019\)R\. Salles, K\. Belloze, F\. Porto, P\. H\. Gonzalez, and E\. OgasawaraNonstationary time series transformation methods: an experimental review\.Knowledge\-Based Systems164,pp\. 274–291\.External Links:ISSN 0950\-7051,[Document](https://dx.doi.org/https%3A//doi.org/10.1016/j.knosys.2018.10.041),[Link](https://www.sciencedirect.com/science/article/pii/S0950705118305343)Cited by:[§1](https://arxiv.org/html/2610.09096#S1.p2.1)\.
- Shaoet al\.\(2024\)Z\. Shao, F\. Wang, Y\. Xu, W\. Wei, C\. Yu, Z\. Zhang, D\. Yao, T\. Sun, G\. Jin, X\. Cao, G\. Cong, C\. S\. Jensen, and X\. ChengExploring progress in multivariate time series forecasting: comprehensive benchmarking and heterogeneity analysis\.External Links:2310\.06119,[Link](https://arxiv.org/abs/2310.06119)Cited by:[Appendix B](https://arxiv.org/html/2610.09096#A2.p1.1),[Table 1](https://arxiv.org/html/2610.09096#S1.T1.4.1.1.1.3.1),[§1](https://arxiv.org/html/2610.09096#S1.p4.1),[§5](https://arxiv.org/html/2610.09096#S5.p8.1)\.
- Spiliotiset al\.\(2020\)E\. Spiliotis, A\. Kouloumos, V\. Assimakopoulos, and S\. MakridakisAre forecasting competitions data representative of the reality?\.International Journal of Forecasting36\(1\),pp\. 37–53\.Note:M4 CompetitionExternal Links:ISSN 0169\-2070,[Document](https://dx.doi.org/https%3A//doi.org/10.1016/j.ijforecast.2018.12.007),[Link](https://www.sciencedirect.com/science/article/pii/S0169207019300159)Cited by:[Appendix A](https://arxiv.org/html/2610.09096#A1.p3.1)\.
- Talagalaet al\.\(2023\)T\. S\. Talagala, R\. J\. Hyndman, and G\. AthanasopoulosMeta\-learning how to forecast time series\.Journal of Forecasting42\(6\),pp\. 1476–1501\.Cited by:[§2](https://arxiv.org/html/2610.09096#S2.p2.1)\.
- Talagalaet al\.\(2022\)T\. S\. Talagala, F\. Li, and Y\. KangFFORMPP: feature\-based forecast model performance prediction\.International Journal of Forecasting38\(3\),pp\. 920–943\.External Links:ISSN 0169\-2070,[Document](https://dx.doi.org/https%3A//doi.org/10.1016/j.ijforecast.2021.07.002),[Link](https://www.sciencedirect.com/science/article/pii/S0169207021001138)Cited by:[§4](https://arxiv.org/html/2610.09096#S4.p2.1)\.
- Tsay \(2005\)R\. S\. TsayAnalysis of financial time series\.John Wiley & Sons\.Cited by:[§1](https://arxiv.org/html/2610.09096#S1.p1.1)\.
- Zenget al\.\(2023\)A\. Zeng, M\. Chen, L\. Zhang, and Q\. XuAre transformers effective for time series forecasting?\.Proceedings of the AAAI Conference on Artificial Intelligence37\(9\),pp\. 11121–11128\.External Links:[Link](https://ojs.aaai.org/index.php/AAAI/article/view/26317),[Document](https://dx.doi.org/10.1609/aaai.v37i9.26317)Cited by:[Appendix B](https://arxiv.org/html/2610.09096#A2.p3.1)\.
- Zeroualet al\.\(2020\)A\. Zeroual, F\. Harrou, A\. Dairi, and Y\. SunDeep learning methods for forecasting covid\-19 time\-series data: a comparative study\.Chaos, solitons & fractals140,pp\. 110121\.Cited by:[§1](https://arxiv.org/html/2610.09096#S1.p1.1)\.
- Zhanget al\.\(2024\)J\. Zhang, X\. Wen, Z\. Zhang, S\. Zheng, J\. Li, and J\. BianProbTS: benchmarking point and distributional forecasting across diverse prediction horizons\.InNeurIPS Datasets and Benchmarks Track,Cited by:[§1](https://arxiv.org/html/2610.09096#S1.p6.1)\.
- Zhaoet al\.\(2026\)Z\. Zhao, J\. Ni, S\. Xu, H\. Liu, W\. Jin, and B\. A\. PrakashTimeRecipe: a time\-series forecasting recipe via benchmarking module level effectiveness\.External Links:2506\.06482,[Link](https://arxiv.org/abs/2506.06482)Cited by:[Appendix B](https://arxiv.org/html/2610.09096#A2.p3.1)\.

## Appendix ALimitations and Future Works

This study was designed to isolate the effect of preprocessing on time series forecasting benchmarks\. Consequently, several design choices should be interpreted as deliberate controls rather than exhaustive coverage of all possible forecasting settings\.

First, the preprocessing search space was restricted to a small set of established, interpretable, and reversible transformations\. This design makes the benchmark controlled and reproducible, while allowing performance differences to be more directly attributed to the preprocessing pipeline\. However, it excludes many other preprocessing strategies that may be relevant in practice, such as moving\-average smoothing, learned normalization, and decomposition\-based methods\. Future work could expand the benchmark to include a richer set of preprocessing techniques, while explicitly distinguishing between reversible transformations, lossy smoothing operations, and representation\-changing transformations\.

Second, all experiments were conducted on univariate time series\. This choice was made to avoid confounding preprocessing effects with cross\-variable dependencies, covariate selection, or the ability of a model to extract information from exogenous variables\. This is also why decomposition\-based methods were not considered\. However, many real\-world forecasting problems are multivariate, and preprocessing may interact differently with models when multiple correlated variables are available\. Future work should therefore extend the benchmark to multivariate forecasting tasks and examine whether the conclusions about structural preprocessing bias remain stable when models can use covariates or multiple target\-related signals\. A similar extension would be valuable for long\-term forecasting settings, where preprocessing choices may affect error accumulation and temporal representation in different ways\. Additionally, while our evaluation utilizes the M4 dataset, we emphasize that this corpus provides a rigorous, large\-scale foundation for analyzing preprocessing sensitivity\. Generating∼5\.1\\sim 5\.1million experimental evaluations, prior PCA and t\-SNE analyses\([Spiliotis et al\., 2020](https://arxiv.org/html/2610.09096#bib.bib33);[Kang et al\., 2020](https://arxiv.org/html/2610.09096#bib.bib25)\)have demonstrated that M4 captures wide variations in autocorrelation, trend strength, spectral entropy, and seasonality, representing a broad and realistic feature space\.

Third, model hyperparameters were largely fixed to make preprocessing the main experimental variable\. This improves interpretability because performance changes can be more directly associated with preprocessing choices rather than model tuning\. However, it also means that the reported rankings should not be interpreted as a fully optimized leaderboard\. Some models may benefit more than others from hyperparameter search, and the best preprocessing pipeline for a model may change when its architecture, learning rate, context length, or regularization parameters are tuned\. A future preprocessing\-aware leaderboard should therefore include model\-specific hyperparameter optimization, while still controlling for fairness and computational budget\.

Finally, the release of the PATM lays the groundwork for future advancements in meta\-learning\. By providing millions of evaluations across diverse models and pipelines, PATM enables researchers to train meta\-models that recommend optimal preprocessing strategies based on time series meta\-features\. We view this as a crucial step toward fully automated, data\-driven forecasting pipelines that dynamically adapt to the statistical structure of any given series\.

## Appendix BBenchmark Literature Review

Robust and standardized benchmarks are essential for evaluating the performance of time series forecasting models, enabling fair comparison and reproducible research\. Historically, large\-scale competitions such as M4 and M5\([Makridakis et al\., 2020](https://arxiv.org/html/2610.09096#bib.bib1)\)have served as crucial benchmarks, providing extensive collections of diverse time series\. Building upon these foundations, the Monash Time Series Forecasting Archive\([Godahewa et al\., 2021](https://arxiv.org/html/2610.09096#bib.bib2)\)expanded the scope by aggregating datasets across varied domains and frequencies\. Recent efforts have focused on providing unified toolkits to handle the increasing complexity of forecasting models\. For instance, TFB\([Qiu et al\., 2024](https://arxiv.org/html/2610.09096#bib.bib3)\)introduces a scalable suite covering multiple domains, emphasizing reproducibility and aspect\-based analysis\. BasicTS\+\([Shao et al\., 2024](https://arxiv.org/html/2610.09096#bib.bib4)\)focuses on benchmarking multivariate forecasting by exploring spatial and temporal heterogeneity\. Furthermore, with the rapid development of foundation models, benchmarks such as GIFT\-Eval\([Aksu et al\., 2024](https://arxiv.org/html/2610.09096#bib.bib5)\)and TSFM\-Bench\([Li et al\., 2025](https://arxiv.org/html/2610.09096#bib.bib6)\)have been designed specifically to evaluate zero\-shot adaptation and prompt\-based forecasting paradigms\.

While the field of benchmarking for time series forecasting is continuously evolving to fill important gaps, a significant limitation persists across most frameworks\. This limitation is the lack of a comprehensive and standardized preprocessing pipeline\. This omission makes direct, fair comparisons between models challenging, as performance gains could be attributed to undisclosed preprocessing steps rather than architectural innovation\. The difference in preprocessing pipelines between benchmarks can cause inconsistent results and add a bias toward models that are robust to different data structures\.

Recent works have started addressing related limitations by exploring model design spaces and evaluating the effectiveness of specific components\. For example,[Zeng et al\. \(2023\)](https://arxiv.org/html/2610.09096#bib.bib10)question the necessity of complex transformer architectures by demonstrating the strength of simple linear models under basic transformations\. Similarly, TimeRecipe\([Zhao et al\., 2026](https://arxiv.org/html/2610.09096#bib.bib35)\)explores the internal architectural design space of deep learning models by benchmarking time series forecasting methods at a finer\-grained module level to uncover optimal configurations\. Although these studies provide valuable insights into model and module selection, they do not yet directly analyze the impact of nonstationary preprocessing on different categories of models\. They also do not explore how this external preprocessing phase impacts each category differently\. This highlights the necessity of a framework that systematically evaluates the interaction between diverse forecasting algorithms and nonstationarity\-handling pipelines\.

## Appendix CTime Series Features

The features stored for PATM provide a high\-dimensional representation of the underlying dynamics of the data\. These features extend the metadata originally distributed with the Monash Time Series Forecasting Archive\([Godahewa et al\., 2021](https://arxiv.org/html/2610.09096#bib.bib2)\)by incorporating additional statistical descriptors, particularly withseasonal\_strength, which quantifies the relative magnitude of seasonal patterns;adf\_pvalue, which captures the statistical significance of the Augmented Dickey–Fuller stationarity test; andskewness, which measures asymmetry in the empirical distribution of observations\. The complete set of features was extracted using thetsfeaturespackage for Python, which implements a wide range of statistical procedures designed to summarize trend, seasonality, autocorrelation structure, complexity, and heteroscedasticity\. Detailed descriptions for each of the 40 extracted features are provided in Table[6](https://arxiv.org/html/2610.09096#A3.T6)\. The subset of features used for visualizations in this study is further described below\.

Table 6:Description of Time Series Features extracted via tsfeatures\.\#Feature NameDescription1meanMean value of the time series\.2varVariance of the time series\.3max\_kl\_shiftMaximum Kullback\-Leibler divergence detected across windows\.4time\_kl\_shiftRelative time index where the maximum KL shift occurs\.5max\_level\_shiftMaximum change in mean level between windows\.6time\_level\_shiftRelative time index where the maximum level shift occurs\.7max\_var\_shiftMaximum variance change between windows\.8time\_var\_shiftRelative time index where the maximum variance shift occurs\.9x\_acf1First autocorrelation coefficient of the original series\.10x\_acf10Sum of squared first 10 autocorrelations of original series\.11diff1\_acf1First autocorrelation of the first\-differenced series\.12diff1\_acf10ACF sum of squares for the first\-differenced series\.13diff2\_acf1First autocorrelation of the second\-differenced series\.14diff2\_acf10ACF sum of squares for the second\-differenced series\.15ARCH\.LMLagrange Multiplier test statistic for ARCH effects\.16crossing\_pointsNumber of times the series crosses the median line\.17entropySpectral entropy measuring the complexity of the series\.18flat\_spotsNumber of sections where the series is relatively constant\.19alphaSmoothing parameter for the level in ETS models\.20betaSmoothing parameter for the trend in ETS models\.21hurstHurst exponent measuring long\-term memory or autocorrelation\.22lumpinessVariance of the variances of tiled windows\.23nonlinearityTeräsvirta’s neural network test for non\-linearity\.24x\_pacf5Sum of squares of the first 5 partial autocorrelations\.25diff1x\_pacf5PACF sum of squares for the first\-differenced series\.26diff2x\_pacf5PACF sum of squares for the second\-differenced series\.27stabilityVariance of the means of tiled windows across the series\.28unitroot\_kpssKPSS test statistic for stationarity of the series\.29unitroot\_ppPhillips\-Perron test statistic for presence of a unit root\.30nperiodsNumber of seasonal periods identified in the data\.31seasonal\_periodLength of the primary seasonal cycle \(e\.g\., 12 for monthly\)\.32trendStrength of the trend component in the decomposition\.33spikeVariance of the error component in a leave\-one\-out analysis\.34linearityLinearity of the trend component from the decomposition\.35curvatureCurvature \(quadratic term\) of the trend component\.36e\_acf1First partial autocorrelation of the remainder series\.37e\_acf10Sum of squared first 10 autocorrelations of the remainders\.38seasonal\_strengthStrength of the seasonal component in the decomposition\.39adf\_pvalueP\-value for the Augmented Dickey\-Fuller test\.40skewnessMeasure of the asymmetry of the data distribution\.Trend and Season\.Trenddescribes the long\-term direction of movement in a time series, whileseasonalityrefers to systematic patterns that repeat over a fixed period\. Using Seasonal and Trend decomposition based on Loess \(STL\)\([Cleveland et al\., 1990](https://arxiv.org/html/2610.09096#bib.bib28)\), a series can be represented as

xt=Tt\+St\+Rt,x\_\{t\}=T\_\{t\}\+S\_\{t\}\+R\_\{t\},whereTtT\_\{t\}is the trend component,StS\_\{t\}is the seasonal component, andRtR\_\{t\}is the remainder\. Based on this decomposition, the strength of trend and seasonality can be measured as

FT=max⁡\(0,1−Var⁡\(Rt\)Var⁡\(xt−St\)\)F\_\{T\}=\\max\\left\(0,\\;1\-\\frac\{\\mathrm\{Var\}\(R\_\{t\}\)\}\{\\mathrm\{Var\}\(x\_\{t\}\-S\_\{t\}\)\}\\right\)and

FS=max⁡\(0,1−Var⁡\(Rt\)Var⁡\(xt−Tt\)\),F\_\{S\}=\\max\\left\(0,\\;1\-\\frac\{\\mathrm\{Var\}\(R\_\{t\}\)\}\{\\mathrm\{Var\}\(x\_\{t\}\-T\_\{t\}\)\}\\right\),respectively\. Values closer to 1 indicate a stronger trend or seasonality, while values closer to 0 indicate a weaker structure\. In this study, high strengths for seasonality and trend is defined as values exceeding 0\.75, while low strength corresponds to values below 0\.25\.

Stationarity\.A series is consideredstrictly stationaryif, for any time shiftsh∈ℤh\\in\\mathbb\{Z\}, and any arbitrary valuesa1,a2,…,ana\_\{1\},a\_\{2\},\\dots,a\_\{n\},

P⁡\(x1≤a1,…,xn≤an\)=P⁡\(x1\+h≤a1,…,xn\+h≤an\)\.P\(x\_\{1\}\\leq a\_\{1\},\\dots,x\_\{n\}\\leq a\_\{n\}\)\\;=\\;P\(x\_\{1\+h\}\\leq a\_\{1\},\\dots,x\_\{n\+h\}\\leq a\_\{n\}\)\.\(3\)
That is, all finite\-dimensional joint distributions are invariant to time shifts\.

A process isweakly stationaryif it has finite second moments and \(i\) its mean functionE⁡\(xt\)E\(x\_\{t\}\)is constant and does not depend on any time indextt, and \(ii\) the covariance of an arbitraryxtx\_\{t\}and time shiftedxt\+hx\_\{t\+h\}depends only onhh\. Weak stationarity is generally sufficient for standard time series modeling\([Box et al\., 2015](https://arxiv.org/html/2610.09096#bib.bib20)\)\.Unless stated otherwise, “stationary” in this report refers to weak stationarity\.To assess this property, we employ the Augmented Dickey–Fuller \(ADF\) test\([Dickey and Fuller, 1979](https://arxiv.org/html/2610.09096#bib.bib27)\), and the decision rule is given in Equation[4](https://arxiv.org/html/2610.09096#A3.E4)\.

Stationarity=\{True,ADF⁡\(X\)≤0\.05,False,ADF⁡\(X\)\>0\.05\.\\mathrm\{Stationarity\}=\\begin\{cases\}\\mathrm\{True\},&\\mathrm\{ADF\}\(X\)\\leq 0\.05,\\\\ \\mathrm\{False\},&\\mathrm\{ADF\}\(X\)\>0\.05\.\\end\{cases\}\(4\)
Entropy\.Spectral entropy measures the complexity or predictability of a time series\. It computes the Shannon entropy of the normalized spectral density of the series\. Values closer to 1 indicate a highly complex and unpredictable series \(similar to white noise\), whereas values closer to 0 indicate a more predictable series with strong structural patterns\. We classify series with an entropy greater than 0\.75 as high entropy and those below 0\.25 as low entropy\.

Shifting\.Shifting captures abrupt structural breaks in the time series, which can manifest as sudden changes in the mean level, variance, or overall distribution\. To quantify shifting, we aggregate features such as the maximum Kullback\-Leibler divergence \(max\_kl\_shift\), maximum level shift \(max\_level\_shift\), and maximum variance shift \(max\_var\_shift\) detected across rolling windows\. Series with significant breaks are categorized as high shifting, while those with stable properties are considered low shifting\.

## Appendix DCategories of Preprocessing

Here,wtw\_\{t\}denotes the transformed series that is closer to a weak stationary series\. The design of our experimental groups was constructed specifically to disentangle the core components of non\-stationarity, such as variance, trend, and seasonality, and observe how their progressive removal interacts with different architectures\. Operations follow a strict mathematical sequence to ensure validity, for example testing scaling in isolation versus combinations of variance stabilization and differencing\.

Variance\-Stabilizing Transforms\.Variance\-stabilizing transforms shrink large values more than small ones, helping residual variance look roughly constant over time\. To stabilize variance that evolves with the mean level of the series, we employ the Box\-Cox Transformation\([Box and Cox, 1964](https://arxiv.org/html/2610.09096#bib.bib29)\)\. This power transformation is a generalization of the logarithmic transform and is defined as:

wt=\{xtλ−1λif​λ≠0ln⁡\(xt\)if​λ=0w\_\{t\}=\\begin\{cases\}\\frac\{x\_\{t\}^\{\\lambda\}\-1\}\{\\lambda\}&\\text\{if \}\\lambda\\neq 0\\\\ \\ln\(x\_\{t\}\)&\\text\{if \}\\lambda=0\\end\{cases\}\(5\)
whereλ\\lambdais the transformation parameter\. Whenλ=0\\lambda=0, the transformation is equivalent to the natural logarithm, which constrains forecasts to be positive on the original scale\. By varyingλ\\lambda, the Box\-Cox transform can address a wide range of heteroscedastic behaviors, ensuring the residual variance remains approximately constant over time\.

Difference\-based Unit Root Removal\.Difference\-based transforms target mean stability by removing changes in level and, with seasonal lags, strong seasonal patterns\. A first\-order differenced series \(Equation[6](https://arxiv.org/html/2610.09096#A4.E6)\) has the difference between consecutive values from the original series, removing linear deterministic trends and converting stochastic trends into a stationary series under standard conditions\.

wt=xt−xt−1\.w\_\{t\}\\;=\\;x\_\{t\}\-x\_\{t\-1\}\.\(6\)
When seasonality of periodmminduces a seasonal unit root, seasonal differencing can convert it into a stationary series by taking themm\-seasonal difference\.

wt=xt−xt−m\.w\_\{t\}\\;=\\;x\_\{t\}\-x\_\{t\-m\}\.\(7\)
Forecasts produced on the differenced scale must be re\-integrated to the original scale by summation of previously differenced values\.

Scaling\.Scaling adjusts the magnitude of the data to ensure that features contribute equally to the model objective function\. While this step is standard, it plays an important role in practice, as many optimization procedures are sensitive to the scale of the inputs, and unscaled data can lead to slower convergence or poorly conditioned objective functions\. The transformation is defined as follows:

wt=xt−μσ,w\_\{t\}=\\frac\{x\_\{t\}\-\\mu\}\{\\sigma\},\(8\)
whereμ\\murepresents the mean andσ\\sigmarepresents the standard deviation of the series\. For forecasting applications, these parameters are typically estimated from the training set to prevent data leakage from the test set\. Similar to other preprocessing steps, the scaling process is invertible, allowing the predicted values to be rescaled to the original units for performance evaluation and interpretation\.

This research employs Z\-Score Normalization\([Pedregosa et al\., 2011](https://arxiv.org/html/2610.09096#bib.bib30)\), which transforms the series to have a mean of zero and a unit variance\.

## Appendix EHardware Specifications

All experiments were conducted on a server equipped with anIntel Xeon Silver 4310 CPU \(2\.10GHz\),512GB DDR4 RAM, and anNVIDIA RTX A6000 \(48GB VRAM\)\. Classical statistical models were implemented usingstatsforecast, while machine learning and deep learning models utilizedscikit\-learn,XGBoost, andPyTorch\.

## Appendix FModel Hyperparameters and Training Configurations

While deep learning models could undoubtedly achieve better absolute accuracy with individualized tuning, our explicit objective in this benchmark is to evaluate the isolated impact of data preprocessing across different model families\. By adopting fixed model hyperparameters and lag settings across all experiments based on established conventions, we strictly isolate preprocessing as the single independent variable\. This ensures that any observed performance shifts are attributable entirely to pipeline conditioning rather than confounding variations in capacity\. Furthermore, while these standardized lookback windows \(input lengths\) were used to maintain experimental control, they were not chosen arbitrarily\. They were adopted directly from the specifications documented by the Monash Time Series Forecasting Archive\([Godahewa et al\., 2021](https://arxiv.org/html/2610.09096#bib.bib2)\)\. Overall, these specifications systematically align the input window length with the temporal frequency and dominant seasonal period of the dataset to provide a consistent evaluation baseline\. As detailed earlier in Table[2](https://arxiv.org/html/2610.09096#S4.T2), this translates to lookback windows that capture the fundamental seasonal cycle, such as 24 steps for hourly series or 7 steps for daily series\. It is important to note that input length does interact with preprocessing\. For example, seasonal differencing requires an input length strictly longer than the seasonal periodmm\. Additionally, deep learning models with fixed context windows might receive slightly different temporal dynamics if aggressive differencing truncates the earliest observations\. A joint exploration of hyperparameter optimization, input lengths, and preprocessing sensitivity remains an important direction for future research\.

### F\.1Statistical Models

For ETS, ARIMA, and Theta, we utilize automated selection procedures to determine the optimal error/trend/seasonal components, lag orders, and smoothing parameters, respectively\. These are implemented via thestatsforecastlibrary using seasonal strength detection\. Automated selection for statistical algorithms is a well\-established practice in benchmark studies\([Godahewa et al\., 2021](https://arxiv.org/html/2610.09096#bib.bib2);[Qiu et al\., 2024](https://arxiv.org/html/2610.09096#bib.bib3);[Aksu et al\., 2024](https://arxiv.org/html/2610.09096#bib.bib5);[Li et al\., 2025](https://arxiv.org/html/2610.09096#bib.bib6)\)\.

### F\.2Machine Learning Baselines

The machine learning baselines, Linear Regression and XGBoost, are configured following standard forecasting benchmarks\.

Table 7:Hyperparameters for Machine Learning BaselinesHyperparameterLinear RegressionXGBoostLibraryscikit\-learnXGBoostMax DepthN/A6EstimatorsN/A1000SubsampleN/A0\.8Colsample bytreeN/A0\.8L2 Regularization \(λ\\lambda\)1\.01\.0
### F\.3Deep Learning and Transformer Architectures

To maintain consistency, neural models were configured such that their capacity is roughly aligned, with the exception of Transformer baselines which follow the recommended configurations from their original publications\.

Table 8:Hyperparameters for Deep Learning ModelsHyperparameterMLPN\-BEATSTimesNetArchitecture2 Hidden Layers6 Stacks / 4 Layers2 Encoder LayersHidden Dim \(dm​o​d​e​ld\_\{model\}\)512256 \(Layer Size\)16FFN Dim \(df​fd\_\{ff\}\)N/AN/A32ActivationReLUReLUGeLU
### F\.4Transformer\-based Architectures

We include PatchTST and Informer as representatives of state\-of\-the\-art attention\-based modeling\. Their hyperparameters follow the standard configurations suggested in their respective original implementations\.

Table 9:Hyperparameters for Transformer\-based ModelsHyperparameterPatchTSTInformerLayers3 Encoder2 Encoder / 1 DecoderAttention Heads164Model Dim \(dm​o​d​e​ld\_\{model\}\)128256FFN Dim \(df​fd\_\{ff\}\)256512ActivationGeLUGeLUNormalizationRevINStandard

## Appendix GLocal vs\. Global Models

In time series forecasting, machine learning and deep learning architectures can be trained using two distinct paradigms, local and global\([Benidis et al\., 2022](https://arxiv.org/html/2610.09096#bib.bib34)\)\. A local model is trained exclusively on a single time series and predicts only for that specific series\. Conversely, a global model is trained jointly across an entire dataset or a large collection of time series\. This global approach allows the model to learn shared patterns and parameters that apply across all instances\.

We decided to run our machine learning and deep learning models in a global setup for our primary evaluation\. This approach aligns directly with standard practices in contemporary forecasting literature\([Nie et al\., 2023](https://arxiv.org/html/2610.09096#bib.bib22)\), where large capacity architectures are typically trained globally to leverage cross\-series information and maximize data availability\.

However, to strictly isolate the per\-series impact of preprocessing pipelines without the potential interference of cross\-series context sharing, we also ran all our experiments locally\. The core results and interpretations remained fundamentally the same across both paradigms\. Under both settings, models without internalized preprocessing continued to exhibit strong sensitivity to external pipelines, while models with internalized mechanisms showed more stable relative performance\. The results currently appearing as Figure[6](https://arxiv.org/html/2610.09096#A7.F6)and Table[10](https://arxiv.org/html/2610.09096#A7.T10)correspond to the experiments evaluated as local models\.

Table 10:Forecasting performance \(MASE\) across preprocessing pipelines and models when trained on each series locally\. Best per model in bold\. Columns in grey are IP\-Models\. Pipelines are composed of:X\(Baseline/None\),V\(Boxcox transformation\),U\(First\-order differencing\),S\(Seasonal differencing\), andQ\(Standard scaling\)\.PipelineARIMAETSTHETALRXGBstMLPNBTSTNetPTSTInformerX2\.352\.252\.222\.894\.552\.942\.482\.292\.2763\.59V3\.192\.382\.363\.774\.546\.422\.492\.262\.2618\.23U2\.232\.402\.602\.282\.733\.013\.023\.273\.082\.35S2\.383\.193\.192\.713\.263\.473\.593\.353\.103\.04Q2\.302\.182\.222\.894\.553\.973\.762\.272\.274\.95VU2\.232\.452\.842\.452\.872\.583\.193\.833\.394\.74VS2\.813\.853\.822\.35​e42\.35e^\{4\}3\.446\.013\.283\.743\.283\.88VQ2\.272\.382\.383\.774\.544\.596\.042\.272\.265\.25US2\.443\.814\.473\.133\.694\.034\.176\.956\.553\.24UQ2\.202\.342\.602\.282\.733\.003\.083\.273\.083\.03SQ2\.393\.133\.192\.713\.263\.613\.513\.363\.103\.33VUS2\.572\.70​e12\.70e^\{1\}2\.99​e42\.99e^\{4\}1\.38​e371\.38e^\{37\}4\.426\.392\.49​e82\.49e^\{8\}1\.23​e61\.23e^\{6\}3\.71​e43\.71e^\{4\}7\.10VUQ2\.332\.452\.852\.452\.873\.213\.443\.623\.353\.33VSQ2\.913\.593\.832\.35​e42\.35e^\{4\}3\.449\.324\.233\.593\.293\.71USQ2\.723\.654\.473\.133\.694\.114\.266\.906\.544\.34VUSQ3\.222\.70​e12\.70e^\{1\}3\.01​e43\.01e^\{4\}1\.38​e371\.38e^\{37\}4\.424\.861\.75​e21\.75e^\{2\}8\.92​e48\.92e^\{4\}3\.29​e43\.29e^\{4\}5\.84

![Refer to caption](https://arxiv.org/html/2610.09096v1/figures/mase_barplot2.png)Figure 6:Barplot MASE of best and oracle pipelines of local models\. Lower loss values mean better results\.
## Appendix HEvaluation Metrics

These metrics capture different aspects of predictive accuracy, such as sensitivity to large deviations, scale dependence, and robustness to varying magnitudes across series\.

Letyiy\_\{i\}denote the true value,y^i\\hat\{y\}\_\{i\}the predicted value, andNNthe total number of evaluated predictions\.

### H\.1Mean Absolute Scaled Error \(MASE\)

Mean Absolute Scaled Error \(MASE\) measures the absolute forecasting error relative to the error of a naive baseline\. For a seasonal time series with seasonality periodmm, the scaling term is computed from the training sequence\{yt\}t=1T\\\{y\_\{t\}\\\}\_\{t=1\}^\{T\}as

Q=1T−m​∑t=m\+1T\|yt−yt−m\|\.Q=\\frac\{1\}\{T\-m\}\\sum\_\{t=m\+1\}^\{T\}\\left\|y\_\{t\}\-y\_\{t\-m\}\\right\|\.\(9\)MASE is then defined as

MASE=1N​∑i=1N\|yi−y^i\|Q\+ϵ,\\mathrm\{MASE\}=\\frac\{1\}\{N\}\\sum\_\{i=1\}^\{N\}\\frac\{\\left\|y\_\{i\}\-\\hat\{y\}\_\{i\}\\right\|\}\{Q\+\\epsilon\},\(10\)whereϵ\\epsilonis a small positive constant for numerical stability\. Whenm=1m=1, the denominator corresponds to the average one\-step naive forecasting error\.

### H\.2Mean Squared Error \(MSE\)

Mean Squared Error \(MSE\) measures the average squared deviation between the predicted values and the ground\-truth observations\. MSE is defined as

MSE=1N​∑i=1N\(yi−y^i\)2\.\\mathrm\{MSE\}=\\frac\{1\}\{N\}\\sum\_\{i=1\}^\{N\}\\left\(y\_\{i\}\-\\hat\{y\}\_\{i\}\\right\)^\{2\}\.\(11\)Because the errors are squared, MSE penalizes large forecasting errors more heavily than small ones\. Lower MSE indicates better predictive accuracy\.

Table 11:Forecasting performance \(MSE\) across preprocessing pipelines and models\. Best per model in bold\. Columns in grey are IP\-Models\. Pipelines are composed of:X\(Baseline/None\),V\(Boxcox transformation\),U\(First\-order differencing\),S\(Seasonal differencing\), andQ\(Standard scaling\)\.PipelineARIMAETSTHETALRXGBstMLPNBTSTNetPTSTInformerChronosX1\.94​e61\.94e^\{6\}9\.96​e69\.96e^\{6\}1\.63​𝒆𝟔\\bm\{1\.63e^\{6\}\}7\.07​e67\.07e^\{6\}2\.21​e62\.21e^\{6\}3\.23​e73\.23e^\{7\}3\.10​e63\.10e^\{6\}1\.95​e61\.95e^\{6\}1\.93​e61\.93e^\{6\}5\.01​e75\.01e^\{7\}1\.60​e61\.60e^\{6\}V2\.35​e62\.35e^\{6\}2\.14​e62\.14e^\{6\}1\.91​e61\.91e^\{6\}9\.16​e89\.16e^\{8\}2\.81​e62\.81e^\{6\}1\.19​e71\.19e^\{7\}3\.14​e93\.14e^\{9\}1\.78​e61\.78e^\{6\}1\.92​e61\.92e^\{6\}6\.26​e76\.26e^\{7\}1\.73​e61\.73e^\{6\}U1\.78​e61\.78e^\{6\}5\.17​e65\.17e^\{6\}4\.76​e64\.76e^\{6\}2\.40​𝒆𝟔\\bm\{2\.40e^\{6\}\}1\.79​e61\.79e^\{6\}2\.76​e62\.76e^\{6\}8\.88​e78\.88e^\{7\}4\.63​e64\.63e^\{6\}6\.29​e66\.29e^\{6\}2\.62​e62\.62e^\{6\}1\.96​e61\.96e^\{6\}S2\.00​e62\.00e^\{6\}3\.82​e63\.82e^\{6\}3\.99​e63\.99e^\{6\}1\.90​e71\.90e^\{7\}1\.83​e61\.83e^\{6\}2\.18​e62\.18e^\{6\}5\.23​e65\.23e^\{6\}3\.65​e63\.65e^\{6\}4\.85​e64\.85e^\{6\}2\.10​e62\.10e^\{6\}2\.24​e62\.24e^\{6\}Q1\.71​𝒆𝟔\\bm\{1\.71e^\{6\}\}3\.53​e63\.53e^\{6\}1\.64​e61\.64e^\{6\}7\.07​e67\.07e^\{6\}2\.85​e62\.85e^\{6\}3\.04​e63\.04e^\{6\}4\.07​e64\.07e^\{6\}1\.77​e61\.77e^\{6\}1\.95​e61\.95e^\{6\}3\.81​e63\.81e^\{6\}1\.60​𝒆𝟔\\bm\{1\.60e^\{6\}\}VU2\.01​e62\.01e^\{6\}2\.93​e62\.93e^\{6\}3\.01​e73\.01e^\{7\}5\.45​e65\.45e^\{6\}1\.72​𝒆𝟔\\bm\{1\.72e^\{6\}\}2\.18​e62\.18e^\{6\}1\.18​e581\.18e^\{58\}7\.98​e87\.98e^\{8\}9\.21​e89\.21e^\{8\}2\.53​e62\.53e^\{6\}2\.14​e62\.14e^\{6\}VS1\.23​e81\.23e^\{8\}8\.83​e118\.83e^\{11\}1\.03​e91\.03e^\{9\}5\.34​e205\.34e^\{20\}1\.86​e61\.86e^\{6\}1\.98​e61\.98e^\{6\}3\.41​e63\.41e^\{6\}2\.87​e82\.87e^\{8\}2\.77​e82\.77e^\{8\}2\.16​e62\.16e^\{6\}2\.76​e72\.76e^\{7\}VQ1\.93​e61\.93e^\{6\}2\.14​𝒆𝟔\\bm\{2\.14e^\{6\}\}1\.88​e61\.88e^\{6\}9\.16​e89\.16e^\{8\}2\.93​e62\.93e^\{6\}3\.68​e63\.68e^\{6\}2\.39​e62\.39e^\{6\}1\.72​𝒆𝟔\\bm\{1\.72e^\{6\}\}1\.85​𝒆𝟔\\bm\{1\.85e^\{6\}\}3\.95​e63\.95e^\{6\}1\.71​e61\.71e^\{6\}US2\.23​e62\.23e^\{6\}7\.01​e67\.01e^\{6\}1\.12​e71\.12e^\{7\}1\.96​e71\.96e^\{7\}3\.63​e63\.63e^\{6\}5\.23​e65\.23e^\{6\}1\.08​e81\.08e^\{8\}2\.48​e72\.48e^\{7\}2\.47​e72\.47e^\{7\}5\.02​e65\.02e^\{6\}6\.46​e66\.46e^\{6\}UQ1\.86​e61\.86e^\{6\}3\.92​e63\.92e^\{6\}4\.76​e64\.76e^\{6\}2\.40​e62\.40e^\{6\}1\.79​e61\.79e^\{6\}1\.99​e61\.99e^\{6\}8\.09​e78\.09e^\{7\}5\.33​e65\.33e^\{6\}5\.73​e65\.73e^\{6\}2\.34​e62\.34e^\{6\}1\.95​e61\.95e^\{6\}SQ2\.03​e62\.03e^\{6\}3\.85​e63\.85e^\{6\}3\.98​e63\.98e^\{6\}1\.90​e71\.90e^\{7\}1\.85​e61\.85e^\{6\}1\.96​𝒆𝟔\\bm\{1\.96e^\{6\}\}2\.13​𝒆𝟔\\bm\{2\.13e^\{6\}\}3\.65​e63\.65e^\{6\}3\.63​e63\.63e^\{6\}2\.01​𝒆𝟔\\bm\{2\.01e^\{6\}\}2\.24​e62\.24e^\{6\}VUS3\.04​e73\.04e^\{7\}5\.66​e115\.66e^\{11\}6\.19​e186\.19e^\{18\}1\.93​e861\.93e^\{86\}7\.25​e77\.25e^\{7\}1\.80​e71\.80e^\{7\}1\.64​e811\.64e^\{81\}9\.06​e209\.06e^\{20\}2\.10​e222\.10e^\{22\}2\.06​e82\.06e^\{8\}7\.87​e137\.87e^\{13\}VUQ2\.39​e62\.39e^\{6\}2\.94​e62\.94e^\{6\}2\.87​e72\.87e^\{7\}5\.45​e65\.45e^\{6\}2\.43​e62\.43e^\{6\}2\.87​e62\.87e^\{6\}1\.03​e581\.03e^\{58\}8\.89​e88\.89e^\{8\}1\.76​e91\.76e^\{9\}3\.38​e63\.38e^\{6\}2\.14​e62\.14e^\{6\}VSQ1\.17​e81\.17e^\{8\}7\.29​e87\.29e^\{8\}1\.01​e91\.01e^\{9\}5\.34​e205\.34e^\{20\}2\.78​e62\.78e^\{6\}2\.58​e62\.58e^\{6\}1\.57​e91\.57e^\{9\}2\.91​e82\.91e^\{8\}2\.28​e82\.28e^\{8\}2\.45​e62\.45e^\{6\}2\.76​e72\.76e^\{7\}USQ2\.96​e62\.96e^\{6\}6\.71​e66\.71e^\{6\}1\.12​e71\.12e^\{7\}1\.96​e71\.96e^\{7\}3\.57​e63\.57e^\{6\}3\.81​e63\.81e^\{6\}4\.71​e64\.71e^\{6\}2\.60​e72\.60e^\{7\}2\.59​e72\.59e^\{7\}4\.82​e64\.82e^\{6\}6\.46​e66\.46e^\{6\}VUSQ1\.75​e91\.75e^\{9\}5\.66​e115\.66e^\{11\}1\.36​e191\.36e^\{19\}1\.93​e861\.93e^\{86\}1\.23​e91\.23e^\{9\}4\.92​e84\.92e^\{8\}1\.78​e811\.78e^\{81\}4\.12​e264\.12e^\{26\}2\.69​e222\.69e^\{22\}4\.97​e94\.97e^\{9\}7\.92​e137\.92e^\{13\}
### H\.3Root Mean Squared Error \(RMSE\)

Root Mean Squared Error \(RMSE\) is the square root of MSE\. It is defined as

RMSE=1N​∑i=1N\(yi−y^i\)2\.\\mathrm\{RMSE\}=\\sqrt\{\\frac\{1\}\{N\}\\sum\_\{i=1\}^\{N\}\\left\(y\_\{i\}\-\\hat\{y\}\_\{i\}\\right\)^\{2\}\}\.\(12\)Unlike MSE, RMSE is expressed in the same unit as the target variable, which makes it easier to interpret\. Similar to MSE, RMSE assigns relatively large penalties to large errors\.

Table 12:Forecasting performance \(RMSE\) across preprocessing pipelines and models\. Best per model in bold\. Columns in grey are IP\-Models\. Pipelines are composed of:X\(Baseline/None\),V\(Boxcox transformation\),U\(First\-order differencing\),S\(Seasonal differencing\), andQ\(Standard scaling\)\.PipelineARIMAETSTHETALRXGBstMLPNBTSTNetPTSTInformerChronosX618\.42648\.65591\.69721\.70661\.901423\.34724\.41670\.77689\.613891\.09593\.42V674\.92610\.30615\.76949\.83685\.92786\.981243\.25642\.18652\.604349\.75624\.72U602\.66661\.07736\.04621\.58615\.27680\.222082\.37882\.41942\.62680\.39593\.82S624\.96804\.39821\.39733\.01629\.87718\.31887\.38806\.01919\.89706\.19657\.58Q610\.05608\.39594\.12721\.61854\.76923\.151025\.95652\.68672\.631026\.64593\.26VU607\.93667\.51815\.84668\.15604\.06685\.636\.40​e266\.40e^\{26\}1446\.611473\.95711\.34614\.74VS707\.486815\.381458\.231\.36​e81\.36e^\{8\}621\.78656\.73673\.551092\.801106\.79695\.86769\.08VQ613\.73610\.16621\.09949\.86863\.521004\.09707\.33648\.06664\.091010\.87606\.99US637\.93991\.671231\.19842\.53759\.16884\.453071\.641797\.691781\.70931\.80890\.15UQ599\.66647\.81736\.40621\.63615\.74631\.411065\.32922\.70898\.47660\.90593\.80SQ625\.38799\.79820\.88733\.13622\.24645\.38660\.50799\.74795\.33649\.58657\.59VUS712\.007559\.641\.51​e71\.51e^\{7\}8\.16​e408\.16e^\{40\}941\.81903\.382\.38​e382\.38e^\{38\}2\.57​e82\.57e^\{8\}1\.07​e91\.07e^\{9\}1137\.145\.44​e45\.44e^\{4\}VUQ634\.77667\.80816\.67668\.17653\.22701\.445\.98​e265\.98e^\{26\}1405\.641744\.87699\.24614\.72VSQ738\.151293\.151452\.541\.36​e81\.36e^\{8\}664\.56682\.761682\.531113\.681020\.35689\.45769\.08USQ709\.20977\.981229\.52842\.55787\.41807\.54882\.531793\.121783\.23864\.65890\.15VUSQ1222\.507565\.953\.07​e73\.07e^\{7\}8\.16​e408\.16e^\{40\}1258\.401073\.742\.48​e382\.48e^\{38\}1\.21​e111\.21e^\{11\}1\.26​e91\.26e^\{9\}1528\.405\.46​e45\.46e^\{4\}
### H\.4Mean Absolute Error \(MAE\)

Mean Absolute Error \(MAE\) measures the average absolute deviation between predictions and observations\. It is defined as

MAE=1N​∑i=1N\|yi−y^i\|\.\\mathrm\{MAE\}=\\frac\{1\}\{N\}\\sum\_\{i=1\}^\{N\}\\left\|y\_\{i\}\-\\hat\{y\}\_\{i\}\\right\|\.\(13\)Compared with MSE and RMSE, MAE is less sensitive to extreme errors because it does not square the residuals\. Lower MAE indicates better forecasting performance\.

Table 13:Forecasting performance \(MAE\) across preprocessing pipelines and models\. Best per model in bold\. Columns in grey are IP\-Models\. Pipelines are composed of:X\(Baseline/None\),V\(Boxcox transformation\),U\(First\-order differencing\),S\(Seasonal differencing\), andQ\(Standard scaling\)\.PipelineARIMAETSTHETALRXGBstMLPNBTSTNetPTSTInformerChronosX526\.24553\.24504\.76614\.33569\.671324\.94620\.81574\.60591\.643833\.70502\.59V581\.59518\.54524\.29731\.96589\.24694\.80852\.16550\.80559\.184296\.38531\.81U512\.02564\.21633\.66526\.75525\.10580\.701842\.06766\.06823\.37581\.06505\.46S531\.41686\.34702\.94618\.88537\.41618\.67767\.10699\.94812\.81603\.85557\.67Q518\.92517\.77507\.36614\.21745\.04826\.66927\.45558\.95578\.99932\.19502\.46VU514\.37570\.43689\.56562\.35515\.75589\.721\.18​e261\.18e^\{26\}1134\.401154\.18612\.51523\.73VS586\.072994\.631139\.414\.90​e74\.90e^\{7\}529\.56561\.19572\.47911\.62921\.35596\.10644\.08VQ519\.82518\.54530\.25731\.99751\.82872\.34605\.18555\.68569\.45903\.31516\.90US543\.87852\.041055\.15717\.05652\.92764\.742591\.421540\.061522\.94807\.85766\.35UQ511\.50553\.24633\.94526\.80525\.82541\.55919\.15802\.22780\.65564\.33505\.44SQ534\.08682\.90702\.50619\.00531\.62553\.43563\.36693\.42689\.04554\.34557\.67VUS602\.113897\.355\.46​e65\.46e^\{6\}2\.88​e402\.88e^\{40\}786\.00768\.823\.56​e373\.56e^\{37\}9\.41​e79\.41e^\{7\}3\.89​e83\.89e^\{8\}920\.592\.24​e42\.24e^\{4\}VUQ541\.44570\.68690\.55562\.37559\.43605\.231\.10​e261\.10e^\{26\}1103\.701334\.46598\.49523\.71VSQ617\.861030\.741136\.644\.90​e74\.90e^\{7\}567\.77584\.371282\.96927\.82856\.77588\.80644\.10USQ608\.37841\.381053\.78717\.07678\.21698\.94759\.871535\.051526\.92748\.18766\.34VUSQ947\.373900\.431\.11​e71\.11e^\{7\}2\.89​e402\.89e^\{40\}981\.56867\.443\.71​e373\.71e^\{37\}4\.36​e104\.36e^\{10\}4\.59​e84\.59e^\{8\}1121\.992\.25​e42\.25e^\{4\}
### H\.5Symmetric Mean Absolute Percentage Error \(sMAPE\)

Symmetric Mean Absolute Percentage Error \(sMAPE\) evaluates the prediction error relative to the magnitude of both the true and predicted values\. It is defined as

sMAPE=100N​∑i=1N2​\|yi−y^i\|\|yi\|\+\|y^i\|\+ϵ,\\mathrm\{sMAPE\}=\\frac\{100\}\{N\}\\sum\_\{i=1\}^\{N\}\\frac\{2\\left\|y\_\{i\}\-\\hat\{y\}\_\{i\}\\right\|\}\{\\left\|y\_\{i\}\\right\|\+\\left\|\\hat\{y\}\_\{i\}\\right\|\+\\epsilon\},\(14\)whereϵ\\epsilonis a small positive constant used to avoid division by zero\. sMAPE is scale\-independent and is commonly reported as a percentage\. Lower sMAPE indicates better forecasting accuracy\.

Table 14:Forecasting performance \(sMAPE\) across preprocessing pipelines and models\. Best per model in bold\. Columns in grey are IP\-Models\. Pipelines are composed of:X\(Baseline/None\),V\(Boxcox transformation\),U\(First\-order differencing\),S\(Seasonal differencing\), andQ\(Standard scaling\)\.PipelineARIMAETSTHETALRXGBstMLPNBTSTNetPTSTInformerChronosX9\.799\.529\.2910\.9310\.1823\.4911\.8310\.3910\.6869\.509\.21V12\.439\.219\.3810\.739\.8812\.1510\.929\.719\.9881\.529\.43U9\.4910\.2912\.259\.739\.8011\.2028\.9614\.3515\.5911\.469\.43S9\.7813\.0913\.5810\.959\.8512\.1815\.6813\.7717\.1613\.2710\.40Q9\.549\.269\.4410\.9212\.8214\.6415\.9310\.0710\.3815\.959\.21VU9\.289\.8411\.159\.679\.3210\.4828\.4713\.1913\.4110\.849\.22VS9\.5812\.2512\.5910\.719\.5010\.0410\.2012\.1612\.3610\.6110\.24VQ9\.399\.209\.3910\.7413\.0214\.9410\.469\.8310\.2115\.179\.24US10\.3315\.9018\.9313\.4412\.8514\.7635\.3824\.1624\.7118\.5414\.57UQ9\.6010\.1612\.259\.739\.769\.8114\.0115\.1914\.5410\.639\.43SQ9\.9312\.9813\.5710\.959\.8510\.3810\.2613\.4413\.7310\.3010\.40VUS9\.8214\.5617\.5212\.1511\.6512\.8534\.2823\.4123\.6813\.1313\.46VUQ9\.489\.8511\.189\.679\.8610\.2711\.8013\.7613\.8610\.509\.22VSQ9\.8612\.2412\.6110\.729\.8410\.1613\.4312\.2112\.3710\.4010\.24USQ11\.9815\.6918\.9113\.4413\.5214\.2916\.1125\.1324\.5214\.3214\.57VUSQ11\.3314\.5617\.5212\.1512\.3212\.5533\.6424\.3823\.7613\.2213\.46

## Appendix IComplementary Results

Tables[11](https://arxiv.org/html/2610.09096#A8.T11),[12](https://arxiv.org/html/2610.09096#A8.T12),[13](https://arxiv.org/html/2610.09096#A8.T13), and[14](https://arxiv.org/html/2610.09096#A8.T14)report forecasting performance when a single preprocessing pipeline is selected and applied uniformly to the entire dataset across MSE, RMSE, MAE, and sMAPE, respectively\. This comprehensive evaluation mirrors the experimental setup described for Table[3](https://arxiv.org/html/2610.09096#S5.T3), providing a broader perspective on model behavior under different loss functions and normalization schemes\.

Across these metrics, the overall trends remain consistent with our primary findings: IP\-Models demonstrate high robustness, typically achieving their peak performance under minimal preprocessing or simple scaling\. In contrast, non\-IP\-Models exhibit more scattered performance, showing a general preference for differencing\-based pipelines \(UUorSS\)\. These patterns hold consistently across both scale\-dependent \(MSE, RMSE, MAE\) and scale\-independent \(sMAPE\) metrics, reinforcing that when architectures lack internal mechanisms to handle nonstationarity, external transformations are critical for optimal performance regardless of the evaluation metric used\.

### I\.1Granular Preprocessing Preferences

Figure[7](https://arxiv.org/html/2610.09096#A9.F7)provides a granular visualization of how often each preprocessing pipeline achieves Top\-3 performance across different data characteristics\. While Table[5](https://arxiv.org/html/2610.09096#S5.T5)highlights the single absolute best pipeline, this heatmap complements those findings by revealing the broader distribution of highly competitive alternatives and the degree of preprocessing sensitivity for each architecture\.

Several new patterns emerge from this expanded view\. First, it highlights the difference between broad robustness and narrow dependence\. Many IP\-Models, such as ARIMA, THETA, and PatchTST, display broad horizontal bands of dark blue across multiple simple pipelines, such asXX,VV,QQ, andV​QVQ\. This indicates that their performance remains highly competitive under various minimal transformations\. Conversely, non\-IP\-Models like Informer, N\-BEATS, and XGBoost often exhibit sharply concentrated preferences, seen as isolated dark blue blocks\. For these architectures, selecting the correct pipeline is critical, as deviating from the optimal choice results in severe performance degradation\.

Second, the heatmap visually captures the migration from simple to complex transformations\. In the Low Trend and Stationary subsets, preference intensity is heavily concentrated on the left side of the grid \(pipelines without differencing\)\. In the High Trend and Non\-Stationary subsets, non\-IP\-Models undergo a massive rightward shift, placing nearly all their preference weight on heavily differenced pipelines such asV​U​QVUQ,U​QUQ, andU​S​QUSQ\.

Finally, the Entropy and Level Shift subplots provide additional nuance\. Under High Entropy environments where series are noisier and more complex, models tend to favor simpler, less aggressive pipelines to avoid amplifying noise\. Conversely, in Low Entropy scenarios with clearer structural predictability, models demonstrate a stronger capacity to leverage complex, multi\-step pipelines successfully\.

![Refer to caption](https://arxiv.org/html/2610.09096v1/figures/heatmap3.png)Figure 7:Relative preference intensity for preprocessing pipelines achieving Top\-3 MASE performance across time series subsets\. Values are row\-normalized per model to highlight the preferred pipelines for each architecture\. Darker blue indicates a higher frequency of Top\-3 performance\.
### I\.2No Pipeline x Oracle Deltas

Table[15](https://arxiv.org/html/2610.09096#A9.T15)reinforces this point by quantifying the percentage gain from the "No Pipeline" to the "Oracle" configuration\. Although the variance is high, reflecting the diversity of time series domains, a clear pattern is observable: models that lack internal preprocessing mechanisms exhibit the largest relative improvements\. In contrast, IP\-Models show comparatively smaller gains, consistent with their architectural design\.

Table 15:MASE for each model across "No Pipeline" and "Oracle" configurations, and percentage gain\. Positive gain means an increase in performance when using "Oracle"\. Grey rows indicate IP\-Models\.ModelMASE \(No Pipeline\)MASE \(Oracle\)Pct Gain \(%\)ARIMA2\.35±\\pm3\.361\.38±\\pm1\.4933\.13±\\pm26\.34ETS2\.25±\\pm3\.611\.44±\\pm1\.6927\.45±\\pm25\.93THETA2\.22±\\pm2\.111\.41±\\pm1\.4629\.17±\\pm27\.34LR2\.87±\\pm5\.961\.48±\\pm1\.6533\.98±\\pm27\.71XGBoost2\.75±\\pm3\.771\.24±\\pm1\.2441\.48±\\pm28\.68MLP31\.88±\\pm116\.601\.13±\\pm1\.0459\.21±\\pm31\.51N\-BEATS4\.65±\\pm44\.231\.13±\\pm1\.0344\.86±\\pm29\.47TimesNet2\.65±\\pm2\.171\.32±\\pm1\.2239\.64±\\pm30\.15PatchTST2\.77±\\pm2\.331\.31±\\pm1\.2441\.39±\\pm30\.48Informer106\.75±\\pm500\.841\.14±\\pm0\.9386\.73±\\pm21\.54Chronos2Synth2\.29±\\pm2\.861\.39±\\pm1\.4031\.39±\\pm25\.68
### I\.3Per\-Model Ranking Analysis

Instead of average rank, Figure[8](https://arxiv.org/html/2610.09096#A9.F8)shows the frequency that each pipeline achieves a certain rank\. This figure gives a more detailed view of the patterns observed on the previous heatmap\. IP\-Models \(except ARIMA\) show a clear preference forXX,VV,QQ, andV​QVQ, where those 4 pipelines achieve Top\-4 more often than any other pipeline\. Non\-IP\-Models, again, have more varied preferences, without a single pattern in common\. XGBoost, Informer, and MLP achieved higher ranks more often when using differencing such asUU,V​UVU,U​QUQ, andV​U​QVUQ\. N\-BEATS follows a similar pattern but also performs well without a preprocessing pipeline\.

![Refer to caption](https://arxiv.org/html/2610.09096v1/figures/n_colorbar2.png)Figure 8:Heatmaps illustrating the distribution of each preprocessing pipeline per Rank across all models\.
### I\.4Quantifying Cost\-Related Trade\-offs

As discussed previously, preprocessing does not significantly increase the computational cost per series\. To thoroughly evaluate this, we compare the cost implications of models trained locally \(one model per series\) versus globally \(one model across all series\)\.

Table[16](https://arxiv.org/html/2610.09096#A9.T16)presents the training time differences between the No Pipeline \(X\) and Oracle configurations under the local training paradigm\. For most models, the absolute difference remains marginal\.

Table 16:Training time comparison between Oracle and No\-Pipeline configurations for local models\.Δ\\Deltais computed as No Pipeline \(X\) minus Oracle\. Grey rows indicate IP\-Models\.ModelOracle Mean \(s\)X Mean \(s\)Δ\\DeltaMean \(s\)Δ\\DeltaStd \(s\)Δ\\Delta\(%\)ARIMA264\.16157\.74\-106\.41531\.22\-40\.28ETS0\.1960\.181\-0\.0150\.054\-7\.75THETA0\.1200\.120\-0\.000030\.0021\-0\.03LR0\.1390\.139\-0\.000090\.0064\-0\.07XGBoost3\.3933\.115\-0\.2771\.161\-8\.17MLP18\.7819\.120\.3381\.9561\.80N\-BEATS24\.8525\.100\.2511\.4021\.01TimesNet175\.32177\.452\.13411\.111\.22PatchTST27\.2727\.620\.3471\.9211\.27Informer196\.23199\.363\.13216\.301\.60When scaling to global models, machine learning and deep learning architectures are trained jointly across the entire dataset\. This global approach amortizes the training cost, allowing models like XGBoost and MLP to become remarkably fast per series\. Figure[9](https://arxiv.org/html/2610.09096#A9.F9)presents the performance versus cost trade\-off for these globally trained models\. In this global regime, deep learning and machine learning models efficiently leverage cross\-series information without suffering the massive overhead of per\-series fitting required by classical methods\.

![Refer to caption](https://arxiv.org/html/2610.09096v1/figures/gpu_global.png)Figure 9:Mean MASE vs\. mean training time for global models\. Marker size indicates peak GPU memory \(baselined at 250MB for CPU\-only models\)\.Table[17](https://arxiv.org/html/2610.09096#A9.T17)quantifies the training time differences in the global paradigm\. Similar to the local results, the absolute time differences remain negligible for almost all models, reaffirming that applying preprocessing pipelines provides a performance boost with virtually no practical impact on training time\.

Table 17:Training time comparison between Oracle and No\-Pipeline configurations for global models\.Δ\\Deltais computed as No Pipeline \(X\) minus Oracle\. Grey rows indicate IP\-Models\.ModelOracle Mean \(s\)X Mean \(s\)Δ\\DeltaMean \(s\)Δ\\DeltaStd \(s\)Δ\\Delta\(%\)ARIMA7\.564\.61\-2\.9488\.68\-63\.83ETS0\.150\.170\.020\.0811\.95THETA0\.130\.130\.000\.082\.56LR0\.120\.12\-0\.000\.00\-0\.15XGBoost0\.070\.06\-0\.020\.01\-28\.89MLP0\.100\.100\.010\.025\.95N\-BEATS0\.290\.25\-0\.040\.03\-15\.21TimesNet2\.782\.890\.111\.833\.65PatchTST0\.340\.29\-0\.060\.03\-19\.13Informer1\.142\.391\.250\.5552\.36

## Appendix JPATM

To support reproducibility and enable metalearning analyses, all experimental outputs are organized into a structured metadataset\. As formalized in Equation[2](https://arxiv.org/html/2610.09096#S3.E2), each record corresponds to a single experimental tuple\(i,j,k\)\(i,j,k\), capturing the interaction between a time series, a preprocessing pipeline, and a forecasting model\.

### J\.1File Organization

The metadataset is distributed as a collection of CSV files, separated by dataset frequency\. For each M4 subset, we provide: \(i\) aPATM file, containing experiment\-level results, and \(ii\) afeature file, containing static descriptors of each time series\.

The complete set of files generated in this study is:

- •patm\_daily\.csv,patm\_hourly\.csv,patm\_quarterly\.csv,patm\_weekly\.csv
- •m4\_daily\_features\.csv,m4\_hourly\_features\.csv,m4\_quarterly\_features\.csv,m4\_weekly\_features\.csv

This separation avoids redundancy, as time series features are invariant across models and preprocessing pipelines, while PATM records are defined per experiment\.

### J\.2PATM Schema

Each row in a PATM file corresponds to a single forecasting experiment\. Table[18](https://arxiv.org/html/2610.09096#A10.T18)summarizes the schema\.

ColumnDescriptionseries\_idUnique identifier of the time seriesmodelForecasting model \(e\.g\., ARIMA, MLP, PatchTST\)pipelineEncoded preprocessing pipeline \(e\.g\., X, VUQ\)transformationVariance\-stabilizing transformation \(V\)diffFirst\-order differencing \(U\) indicatorsdiffSeasonal differencing \(S\) indicatorscalerScaling method \(Q\)mape,mse,rmse,mae,smape,maseForecasting performance metricsforecastSerialized forecast output \(test horizon\)timeTraining and inference timegpu\_peak\_memory\_mbPeak GPU memory usage \(MB\)seedRandom seedpidProcess identifieruuidUnique experiment identifierTable 18:Schema of the Preprocessing\-Aware Time Series Metadataset \(PATM\)\.The schema captures both predictive performance and computational cost, enabling multi\-objective evaluation\.

### J\.3Example Record

An example row from a PATM file is shown below:

```
series_id: 1
model: PatchTST
pipeline: none-diff-none-none
transformation: none
diff: diff
sdiff: none
scaler: standard_scaler
mape: 0.018365ΨΨΨΨΨ
mse: 24334.813340
rmse: 155.996196
mae: 124.343401
smape: 1.819308
mase: 0.823671
forecast: [6852.52620975, 6859.60718623, 6883.1543111, ...]
time: 1.299543
gpu_peak_memory_mb: 370.0
seed: 42
pid: 807252
uuid: 0acce284-26da-43b9-8c33-68dde290e4d9
```

This entry indicates that the PatchTST model was trained on series 1 using a pipeline composed of first\-order differencing \(U\)\.

### J\.4Feature Files

Eachm4\_<frequency\>\_features\.csvfile contains one row per time series, with the full set of descriptors described in Appendix[6](https://arxiv.org/html/2610.09096#A3.T6)\. These features can be joined with PATM files via theseries\_idfield, enabling analyses of how time series characteristics influence preprocessing effectiveness and model performance\.

#### Usage\.

The metadataset can be interpreted as a relational structure where PATM defines experiment\-level observations and feature files define series\-level attributes\. This design supports meta\-learning, preprocessing recommendation, and performance modeling tasks\.