ARMA Block: A CNN-Based Autoregressive and Moving Average Module for Long-Term Time Series Forecasting

Il Dong Yun; Myung Jin Kim; YeongHyeon Park

REVIEW 4 major objections 5 minor 19 references

ARMA Block: A CNN-Based Autoregressive and Moving Average Module for Long-Term Time Series Forecasting

T0 review · 4 major / 5 minor · reviewed 2026-08-04 · deepseek-v4-flash

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

Pith's one-line read A two-convolution ARMA block—one layer trends, one layer fixes residuals—matches or beats transformer and linear baselines on long-term forecasting, especially when trends shift.

desk verdict Simple ARMA-inspired block, but the headline results are confounded by RevIN and the architecture may be a linear map in disguise. read the letter →

arxiv 2509.10324 v1 pith:XW4BD7AV submitted 2025-09-12 cs.LG

Myung Jin Kim , YeongHyeon Park , Il Dong Yun This is my paper

classification cs.LG

keywords timeseriesforecastingCNNARIMA-inspiredautoregressivemovingaveragelong-termtrendshiftpositionalinformationresiduallearning

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper proposes a simple, parameter-light module for long-term time series forecasting, inspired by ARIMA but built from two small convolutional filters. One filter (AR) predicts the overall trend directly from the input; the second (MA) takes the input minus the AR prediction and refines the high-frequency residual details. The output is the sum of the two. The authors claim that on nine standard benchmark datasets, this module achieves state-of-the-art or highly competitive accuracy, with particular strength on datasets exhibiting trend shifts and distributional non-stationarity such as Exchange, ILI, ETTh2, and ETTm2. They also claim the trained CNN filters inherently encode absolute positional information, suggesting the block could substitute for explicit positional embeddings in sequential models.

What carries the argument

The ARMA block: two small convolutional filters (in the experiments, 5×5) operating in a residual manner. The AR filter maps the input sequence directly to the forecast, learning the trend. The residual input minus the AR output is fed to the MA filter, which learns to correct local, high-frequency deviations. The final forecast is the sum of the two filter outputs. The design is direct multi-step (no iterative rolling forecast), which makes it multivariate-friendly, and it is paired with RevIN normalization to handle non-stationarity.

What would settle it

Retrain DLinear, NLinear, FEDformer, Autoformer, and the ARMA block under identical training pipeline, normalization, and model-selection policy on the four trend-shift datasets; if the ARMA block no longer matches or beats the best baseline on multiple horizons, the paper's central claim lacks support. Similarly, remove the padding from the trained CNN filters and re-test position-index prediction; if accuracy collapses, the claim that CNNs inherently encode absolute position for this block is refuted.

Watch

Extended reading notes

Core claim

The central claim is that a residual two-branch convolutional design y_out = AR(x_in) + MA(x_in − AR(x_in)) yields forecasts that are on par with or better than established linear and transformer baselines across a range of long-term forecasting benchmarks, and that it excels specifically on non-stationary trend-shift datasets. The AR branch is argued to capture the evolving trend because the optimizer first follows the larger-gradient trend signal, while the MA branch corrects the remaining detail. Additionally, the paper argues that the CNN filters themselves encode absolute positional information—shown by training a single linear layer on frozen CNN features to predict linear, gradation,

Load-bearing premise

The conclusion that the ARMA block is competitive or state-of-the-art rests on comparing the authors' single configuration against published baseline numbers that were obtained under different training pipelines and selection policies, with no documented shared preprocessing or protocol.

Editorial extensions

If this is right

On trend-shift datasets (Exchange, ILI, ETTh2, ETTm2), the ARMA block achieves the best or highly competitive results across multiple forecasting horizons, surpassing both transformer and linear baselines.
The module can be integrated as a drop-in component into other architectures, offering a low-complexity alternative to structured state-space modules or transformer-based forecasting heads.
Because the CNN filters carry absolute positional information, models using the ARMA block can omit explicit positional embeddings, reducing model complexity.
The ablation study on ILI shows that removing the MA branch raises error (MSE from 1.353 to 1.699), supporting the claim that the residual correction materially improves forecast detail.
The block's direct multi-step forecasting, unlike iterative ARIMA, makes it readily usable in multivariate forecasting pipelines.

Reading between the lines

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

If the positional-information claim transfers to deeper or wider CNN stacks, the ARMA block could serve as a general-purpose positional-encoding replacement not just for forecasting but for other sequence modeling tasks where absolute position matters.
The residual decomposition implicitly acts as a trainable differencing operator; one could test whether extending it to multiple AR/MA stages (a higher-order ARMA) further improves accuracy on strongly non-stationary series without losing the module's simplicity.
The paper's comparison relies on published baseline numbers rather than a unified training pipeline; a direct head-to-head with all baselines retrained under the same normalization, horizon, and selection protocol would clarify whether the trend-shift advantage is intrinsic to the architecture or an artifact of evaluation conditions.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague, quick take on arXiv:2509.10324. The ARMA block is a simple residual two-branch CNN module that predicts trend and residual separately, inspired by ARIMA. That specific direct multi-step residual formulation looks new relative to the cited work. The paper is also refreshingly honest in the conclusion: it doesn't always beat recent linear baselines. The ablation on ILI shows the MA branch helps over a single CNN.

But the central 'state-of-the-art on trend-shift datasets' claim doesn't hold up as presented. Table 1 compares ARMA+RevIN against baselines taken from prior papers with SAN and 'best only' numbers. The datasets where ARMA wins—Exchange, ILI, ETTh2, ETTm2—are exactly the non-stationary ones where RevIN is known to give big gains. Without a same-normalization comparison, you can't tell if the block or the RevIN is doing the work. The ablation keeps RevIN throughout, so it doesn't resolve this.

Second, the paper never says whether the convs have an activation. If they don't, y_out = (A+B-BA)x, one linear map. The 'AR captures trend, MA fixes details' story is then a story, not a mechanism. At minimum the authors should state the nonlinearity or admit the block is a linear operator with a particular factorization.

Third, the positional probe (train a linear layer on frozen conv features to predict index signals) is suggestive but has no null control. You'd want a random CNN or an MLP baseline to know whether the position information is specific to this block. It also isn't shown to improve forecasting.

Methodologically, there are no error bars, no seeds, no code, and the baseline selection is opaque. These are fixable in revision. The idea is cheap and modular, and the paper is short and readable. I'd say give it a serious referee if the authors are willing to redo the comparison with matched normalization and clarify the linearity. Right now, treat the headline results as unverified.

Referee Report

4 major / 5 minor

Summary. The paper proposes the ARMA block, a two-branch convolutional module for long-term multivariate time series forecasting. The block computes y_ar = AR(x_in) and y_ma = MA(x_in - y_ar), then outputs y_out = y_ar + y_ma, motivated by ARIMA but designed for direct multi-step forecasting. Experiments on nine benchmarks compare this module (with RevIN normalization) against five baselines, and a probe experiment attempts to show that the trained CNN features encode absolute positional information. The central claims are that the block is highly competitive or state-of-the-art on trend-shift datasets (Exchange, ILI, ETTh2, ETTm2) and that it inherently encodes positional information.

Significance. If properly validated, the ARMA block would be a useful contribution: it is simple, parameter-light, easy to integrate, and the claimed robustness to non-stationary trend shifts would be practically valuable. The architecture description is clear, and the qualitative decomposition into trend and detail components is intuitive. However, the current experimental evidence does not isolate the contribution of the ARMA structure from normalization choices, and the comparison set is too narrow to support the 'state-of-the-art' wording. The positional-information probe is suggestive but under-specified and not tied to forecasting utility. The contribution is therefore conditional on a substantially strengthened evaluation.

major comments (4)

[Section 3.1 / Table 1] The evaluation is confounded. The ARMA model uses RevIN (Section 3.1), while baseline numbers are taken from prior papers and are marked 'best only'; some use SAN and some do not (Table 1 footnote). No shared training pipeline, normalization, or selection policy is documented. Because RevIN is known to produce large gains precisely on non-stationary data, the fact that ARMA wins on Exchange, ILI, ETTh2, and ETTm2 may reflect the normalization rather than the two-branch architecture. The paper must report ARMA with and without RevIN, and compare against baselines trained under identical normalization and evaluation conditions, ideally in a shared code base with multiple seeds.
[Section 3.4 / Table 3] The ablation study is insufficient to attribute the reported gains to the ARMA block. It is performed on only one dataset (ILI), at one horizon (36, matching Table 1), and it removes only the MA branch while keeping RevIN. This cannot separate the effect of the two-branch residual structure from the effect of RevIN, nor does it show that the AR branch alone is a proper control. I recommend ablations on all four trend-shift datasets, including a RevIN-only linear model, a single CNN branch with and without RevIN, and the full ARMA block with and without RevIN.
[Section 3.2 / Table 2] The positional-information claim is supported only by a linear probe on one frozen model, with no description of the probe targets beyond 'linear index, gradation, sinusoid signal' and no comparison to untrained or randomly initialized CNNs. The result that a linear readout can reconstruct synthetic signals from CNN features may simply reflect the choice of probe and the specific dataset. The conclusion that the block 'inherently encodes absolute positional information' and could replace positional embeddings goes beyond the evidence. Please specify the probe protocol in detail, include negative controls, and preferably demonstrate that the encoded position information contributes to forecasting performance.
[Section 3.3 / Conclusion] The 'state-of-the-art' and 'most recent linear baselines' claims are not supported by the baseline set. Table 1 includes only DLinear/NLinear (2023), FEDformer (2022), Autoformer (2021), and Informer (2021). No comparison is made with PatchTST, iTransformer, TimesNet, or recent normalization-aware linear models. Given the paper's own conclusion says 'state-of-the-art results in several cases,' the comparison should be updated to include modern baselines under a shared protocol, or the claims should be softened to 'competitive with the five listed baselines under the reported settings.'

minor comments (5)

[General / Title] The title in the full text has an unusual space in 'A VERAGE' (likely a typo), and there are duplicate captions for Fig. 2 in Section 2.
[Section 2 / Fig. 1] Please specify the exact convolution dimensions. The paper says '5x5 filter,' but for multivariate 1D time series it is unclear whether this is a 1D convolution with kernel size 5 across the time dimension, a 2D convolution over time and channels, or something else. Padding, strides, and channel widths should be stated.
[Section 3.1] Training details are sparse beyond batch size and learning rate. Please report number of epochs, early-stopping criteria, validation selection, input sequence lengths per dataset (especially ILI), and the number of runs used for averaging.
[Table 3] The table does not identify the dataset or horizon; from Table 1 it appears to correspond to ILI horizon 36. Please state this explicitly.
[Table 2] The MAE values for 'Linear index' and 'Gradation' are both 0.0017; reporting three decimals is insufficient to compare. Also, define the target signals precisely (e.g., length, range, whether the probe predicts a scalar per time step or a per-channel signal).

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: ARMA forecasts are empirical benchmark results with no fitted-parameter-as-prediction, no load-bearing self-citation, and no derivation-by-construction.

full rationale

The paper's derivation chain is a straightforward architecture definition followed by empirical evaluation. Equations (1)-(3) define the ARMA block as y_out = AR(x_in) + MA(x_in - AR(x_in)); this is a construction, not a fitted quantity relabeled as a prediction. The position-information analysis (Section 3.2) trains a linear probe on frozen CNN features using synthetic position labels and evaluates on held-out test data, so it is a standard representational probe rather than a circular fit. No load-bearing self-citations or imported uniqueness theorems appear; the only external citations are ordinary related-work references. The skeptical concern about RevIN/SAN baseline comparability (Section 3.1, Table 1 footnote) is a threat to the validity of the empirical comparison, but it is not a circular derivation: the reported forecast errors are measured outcomes, not quantities equivalent to the inputs by construction. Likewise, the MA branch's dependence on the AR residual is a deliberate architectural design, and the ablation in Table 3 compares the full module against an AR-only CNN under identical training, which is an empirical test rather than a tautology. No circular step can be exhibited from the paper's equations or claims.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

All ledger entries are assumptions the paper does not prove. The comparability of copied baseline numbers is the most load-bearing for the empirical claim; the semantic AR/MA role split and the positional-encoding transfer from [11] are secondary. No independent invented entities are introduced: the ARMA block is a model component, not an external postulate.

free parameters (4)

Filter size (AR/MA convolution) = 5x5
Hand-selected in Section 3.1; no sweep or ablation of receptive field is reported, despite this being the core mechanism of the block.
Learning rate = 0.001
Set in Section 3.1; no search or sensitivity analysis is reported.
Batch size = 32
Set in Section 3.1; no search or sensitivity analysis is reported.
Model width, depth, padding, and activation = not reported
The architecture section omits the number of filters, number of layers, padding, stride, and activation function, all of which are required to reproduce the accuracy claims and to determine whether the AR/MA decomposition is meaningful.

assumptions (4)

domain assumption Baseline errors in Table 1, copied from prior papers and marked 'best only' with SAN, are directly comparable to the authors' single ARMA configuration.
Section 3.3 and Table 1 footnote; the entire competitive claim depends on this comparability, but no shared pipeline, normalization, or selection policy is provided.
ad hoc to paper The CNN branches will learn semantically separable roles during optimization: AR captures trend, MA captures residual detail.
Sections 2.1-2.2 and Fig. 2; the role split is asserted from gradient-magnitude intuition and one correlation plot, not guaranteed by the architecture.
domain assumption CNNs encode absolute position from padding, and this property transfers to the ARMA block.
Section 3.2 relies on [11] for this property without testing the ARMA block against a null model or an untrained-feature baseline.
ad hoc to paper Convolutional branches have the padding and activation setup needed to make the AR/MA split and positional claims meaningful.
Section 2 does not specify padding or activation; if the branches are linear, y_out = (A+B-BA)x and the AR/MA role split is unidentifiable.

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Cite this review

Pith. "Pith review of ARMA Block: A CNN-Based Autoregressive and Moving Average Module for Long-Term Time Series Forecasting." pith.science (2026). https://pith.science/paper/XW4BD7AV

@misc{pith2026250910324,
  author       = {Pith},
  title        = {Pith review of: ARMA Block: A CNN-Based Autoregressive and Moving Average Module for Long-Term Time Series Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XW4BD7AV}},
  note         = {Machine review of arXiv:2509.10324}
}

read the original abstract

This paper proposes a simple yet effective convolutional module for long-term time series forecasting. The proposed block, inspired by the Auto-Regressive Integrated Moving Average (ARIMA) model, consists of two convolutional components: one for capturing the trend (autoregression) and the other for refining local variations (moving average). Unlike conventional ARIMA, which requires iterative multi-step forecasting, the block directly performs multi-step forecasting, making it easily extendable to multivariate settings. Experiments on nine widely used benchmark datasets demonstrate that our method ARMA achieves competitive accuracy, particularly on datasets exhibiting strong trend variations, while maintaining architectural simplicity. Furthermore, analysis shows that the block inherently encodes absolute positional information, suggesting its potential as a lightweight replacement for positional embeddings in sequential models.

Figures

Figures reproduced from arXiv: 2509.10324 by the authors.

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Reference graph

Works this paper leans on

19 extracted references · 3 linked inside Pith

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Time series forecasting has moved beyond simply predicting weather or traffic, and is being used to learn patterns from any data that has an order to produce results

INTRODUCTION Recently, the Time Series Forecasting (TSF) has become an increasingly important area. Time series forecasting has moved beyond simply predicting weather or traffic, and is being used to learn patterns from any data that has an order to produce results. For example, the Transformer [1] has been successful in the field of natural language proc...
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The block diagram is arXiv:2509.10324v1 [cs.LG] 12 Sep 2025 shown in Fig 1

METHOD This section explains the structure of the Auto Regressive Moving Average (ARMA) block. The block diagram is arXiv:2509.10324v1 [cs.LG] 12 Sep 2025 shown in Fig 1. The block is simple, consisting of two CNN components and a bias. Each part predicts the trend and de- tails separately. Although it appears structurally similar to DLinear, the underlyi...

arXiv 2025
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EXPERIMENTS 3.1. Experiments Settings Dataset.We conduct extensive experiments on nine widely- used multivariate real-world datasets, including ETT (Elec- tricity Transformer Temperature) [5] (ETTh1, ETTh2, ETTm1, ETTm2), Traffic, Electricity, Weather, ILI, ExchangeRate [13]. All of them are often used multivariate time series. Training environments.We ad...
[4]

CONCLUSION We presented the ARMA block, a simple forecasting mod- ule that combines efficiency, robustness, and adaptability. By capturing both long-term trends and high-frequency residuals, the block is particularly effective on datasets with trend shifts, achieving state-of-the-art results in several cases. While its accuracy does not always surpass tha...
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Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.

[1] [1]

Time series forecasting has moved beyond simply predicting weather or traffic, and is being used to learn patterns from any data that has an order to produce results

INTRODUCTION Recently, the Time Series Forecasting (TSF) has become an increasingly important area. Time series forecasting has moved beyond simply predicting weather or traffic, and is being used to learn patterns from any data that has an order to produce results. For example, the Transformer [1] has been successful in the field of natural language proc...

[2] [2]

The block diagram is arXiv:2509.10324v1 [cs.LG] 12 Sep 2025 shown in Fig 1

METHOD This section explains the structure of the Auto Regressive Moving Average (ARMA) block. The block diagram is arXiv:2509.10324v1 [cs.LG] 12 Sep 2025 shown in Fig 1. The block is simple, consisting of two CNN components and a bias. Each part predicts the trend and de- tails separately. Although it appears structurally similar to DLinear, the underlyi...

arXiv 2025

[3] [3]

EXPERIMENTS 3.1. Experiments Settings Dataset.We conduct extensive experiments on nine widely- used multivariate real-world datasets, including ETT (Elec- tricity Transformer Temperature) [5] (ETTh1, ETTh2, ETTm1, ETTm2), Traffic, Electricity, Weather, ILI, ExchangeRate [13]. All of them are often used multivariate time series. Training environments.We ad...

[4] [4]

CONCLUSION We presented the ARMA block, a simple forecasting mod- ule that combines efficiency, robustness, and adaptability. By capturing both long-term trends and high-frequency residuals, the block is particularly effective on datasets with trend shifts, achieving state-of-the-art results in several cases. While its accuracy does not always surpass tha...

[5] [5]

Attention is all you need,

Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin, “Attention is all you need,”Ad- vances in neural information processing systems, vol. 30, 2017

2017

[6] [6]

An image is worth 16x16 words: Trans- formers for image recognition at scale,

Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszkoreit, and Neil Houlsby, “An image is worth 16x16 words: Trans- formers for image recognition at scale,” inInternational Conference on Learning Representations, 2021

2021

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Mamba: Linear-time sequence modeling with selective state spaces,

Albert Gu and Tri Dao, “Mamba: Linear-time sequence modeling with selective state spaces,”arXiv preprint arXiv:2312.00752, 2023

arXiv 2023

[8] [8]

Mamba: Linear-time sequence modeling with selective state spaces,

Albert Gu and Tri Dao, “Mamba: Linear-time sequence modeling with selective state spaces,” inFirst Confer- ence on Language Modeling, 2024

2024