Data Compression for Time Series Modelling: A Case Study of Smart Grid Demand Forecasting

Akanksha Upadhyay; Mikkel Bendixen Copeland; Mikkel Bue Lykkegaard; Philipp Tr\'enell; Svend Vendelbo Nielsen

REVIEW 3 major objections 6 minor 34 references

Data Compression for Time Series Modelling: A Case Study of Smart Grid Demand Forecasting

T0 review · 3 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Careful wavelet-based lossy compression can remove 99% of a smart-grid sensor stream without degrading forecast skill, and normalized mutual information tells you where the safe limit is.

desk verdict A competent, clearly-written applied study whose main robustness claim is likely true but is measured with a train-on-compressed/test-on-uncompressed protocol that doesn't match real deployment. read the letter →

arxiv 2505.02606 v1 pith:RY6RHFE7 submitted 2025-05-05 cs.CE

Mikkel Bue Lykkegaard , Svend Vendelbo Nielsen , Akanksha Upadhyay , Mikkel Bendixen Copeland , Philipp Trénell This is my paper · ORCID

classification cs.CE

keywords timeseriesforecastinglossycompressiondiscretewavelettransformbiorthogonalwaveletsnormalizedmutualinformationsmartgridXGBoostdemand

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to establish that wavelet-based lossy compression of high-frequency sensor data can cut storage and transmission volume dramatically without destroying forecasting accuracy, as long as the wavelet, compression rate, and model are chosen with care. It tests five biorthogonal wavelets at compression rates from 0.4 to 0.999 on seawater-intake forecasts from a Danish port, comparing a linear regression model, XGBoost, and TiDE. XGBoost's forecast error stays nearly flat up to 99% compression, while the linear model collapses under smooth wavelets and TiDE remains competitive but variable. Normalized mutual information, fitted to a regularized incomplete beta curve, tracks how much signal survives compression and gives a practical warning that predictive error is about to spike. The paper also states its own limitation: lossy compression can irreversibly discard features that later prove useful for other downstream tasks such as anomaly detection and diagnostics.

What carries the argument

The carrying object is the Discrete Wavelet Transform (DWT) with biorthogonal spline wavelets, indexed as BiorNr.Nd, where the analysis and synthesis filters are dual rather than identical, allowing perfect reconstruction with asymmetric designs. Thresholding small detail coefficients produces a sparse representation, and the lossy compression rate is defined as $r_{\mathrm{lossy}}=N_0/N_Y$, the fraction of zeroed coefficients. The guiding metric is Normalized Mutual Information, $\mathrm{NMI}(r)=I(\tilde{Y}_r;Y)/I(\tilde{Y}_0;Y)$, whose decline with compression is compressed into two parameters by fitting $1-I_r(\alpha,\beta)$, a regularized incomplete $\beta$ function. This machinery supplies both the data reduction and the early-warning signal: the DWT creates the compressed training data, while the NMI curve, especially its sharp drop near $r\to 1$, predicts where forecast error for the stable gradient-boosted model begins to climb.

What would settle it

Run the identical experiment with the test set compressed at the same rate and with the same wavelet as the training set, and compare the linear model's RMSE with Table 2; if Bior6.8 at $r=0.6$ no longer gives errors around 6372, the train/test mismatch rather than the wavelet caused the collapse. A second check is to test on an independent dataset whether the fitted NMI elbow, the point where $1-I_r(\alpha,\beta)$ starts falling steeply, predicts the compression rate at which XGBoost RMSE begins to climb.

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Extended reading notes

Core claim

The central claim is that Discrete Wavelet Transform compression can keep the information needed for accurate one-to-six-hour forecasts of water intake level even when 99% of the wavelet coefficients are zeroed, and that Normalized Mutual Information (NMI) quantifies when compression starts erasing task-relevant information. With XGBoost, RMSE remains close to its uncompressed baseline from $r=0.4$ through $r=0.99$ across all five biorthogonal wavelets, with noticeable degradation only at $r=0.999$. The linear model performs best on uncompressed data but its error explodes with smooth wavelets, reaching an RMSE near 6372 for Bior6.8 at $r=0.6$, because training on smoothed short-lag inputs leaves it sensitive to high-frequency perturbations in the uncompressed test data. TiDE shows no clear pattern but stays competitive except at the most extreme compression. The paper frames NMI as a dimensionless, bounded measure of retained signal strength, fits it as $\mathrm{NMI}(r)=1-I_r(\alpha,\beta)$, and recommends an elbow-style rule on the NMI or RMSE curve to choose a safe compression rate before errors rise sharply. It explicitly acknowledges that lossy compression may irreversibly discard features useful for other downstream applications.

Load-bearing premise

The load-bearing premise is that training a model on compressed data but testing it on uncompressed data mirrors real deployment; if the live data were also compressed at the same rate, the extreme failures of the linear model under smooth wavelets would probably disappear.

Editorial extensions

If this is right

If the claim holds, a one-minute seawater-supply sensor stream can be stored or transmitted at 1% of its raw size while an XGBoost forecaster keeps six-hour intake-level errors close to its uncompressed baseline.
Because lossless Brotli compression only reaches $r=0.36$, lossy wavelet compression becomes practically useful only above that rate; the study's tested range of $0.4$ to $0.999$ covers the regime that matters.
Wavelet choice is task-dependent: rough wavelets such as Bior1.1 preserve sharp transitions, while smooth wavelets such as Bior6.8 retain medium-frequency oscillations but introduce Gibbs artifacts near discontinuities, so the wavelet should be matched to the signal's structure.
NMI curves fitted as $1-I_r(\alpha,\beta)$ can be combined with an elbow rule to select a compression rate before the sharp RMSE rise, yielding an operational stopping criterion for data pipelines.
The paper's stated limitation stands: lossy compression may permanently discard features needed later for anomaly detection, diagnostics, or alternative models, so retention decisions should account for the broader ecosystem of data uses.

Reading between the lines

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

The dramatic linear-model failures under Bior3.9 and Bior6.8 likely depend on the train-on-compressed, test-on-uncompressed protocol; if live data were compressed at the same rate as the training data, a regularized linear model might remain usable at moderate compression. The paper mentions smoothing the test data as a possible mitigation but does not test it.
The NMI-to-RMSE relationship for XGBoost suggests a testable edge-sensor design rule: compute a rolling NMI estimate on compressed batches and reduce the compression rate whenever NMI nears its sharp-drop region, rather than fixing a single rate in advance.
Because the error threshold couples NMI with model class, a linear model would likely require a more conservative NMI floor than XGBoost; one concrete test is to find, for each model, the NMI value at which RMSE rises by a fixed factor and use that as a model-specific compression budget.
The method should port to other high-frequency forecasting domains such as wind power or electricity prices, but the optimal wavelet order will probably shift with signal roughness, so the portable finding is the NMI-guided selection procedure rather than any specific Bior order.

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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

Quick take: this is a competent applied study with a modest new contribution. The main thing you should know is that the central claim—XGBoost stays accurate under heavy wavelet compression—is probably true, but the paper's evaluation protocol doesn't actually test the deployment scenario it claims to address.

What's new: systematic comparison of five biorthogonal wavelets across compression rates 0.4–0.999 for three forecasting models on a real smart-grid-like dataset. DWT compression for forecasting is not new (refs 9 and 23 cover that), and the models are off-the-shelf. The new bits are the NMI-based heuristic for picking a compression rate and the explicit robustness framing. Those are legitimate extensions, not a method breakthrough.

What's done well: the experiments are clearly described. The NMI metric is a sensible way to quantify information retention. The authors are honest about limitations, including the potential loss of information for downstream tasks and the fact that smoothing the test data could mitigate OLS sensitivity. They acknowledge LLM writing assistance, which is refreshing. The XGBoost robustness result is consistent across Table 2, even with the protocol caveat.

Soft spots: the train-on-compressed/test-on-uncompressed protocol (Section 3.2) is the big one. In a real edge-compression pipeline, if you compress for storage or transmission, the inference-time inputs are also reconstructed from the same lossy representation. Training on compressed and testing on raw data measures distribution shift, not the compression/forecast tradeoff. The paper itself notes smoothing test data as a mitigation but doesn't adopt it. The headline OLS collapse (RMSE 6373 at bior6.8, r=0.6) is mostly an artifact of this shift. XGBoost may well survive a deployment-consistent protocol, but as reported the quantitative tradeoff is not validated for the intended use case.

Other issues: no error bars on the aggregate metrics, no hyperparameters for XGBoost or TiDE, no code or data release. The NMI elbow heuristic is demonstrated only for XGBoost. These are fixable but need to be addressed.

Who is this for: practitioners in smart grid or IoT settings who want a rough recipe for how much wavelet compression a tree-based forecaster can tolerate. That recipe is probably serviceable, but I wouldn't generalize beyond this site.

Recommendation: this deserves peer review—it's a serious empirical study with a clear question—but it needs a major revision first. The authors should add a deployment-consistent evaluation, report error bars and hyperparameters, and either release code/data or explain why not. I'd write a supportive but demanding referee report.

Referee Report

3 major / 6 minor

Summary. The paper investigates the impact of discrete wavelet transform (DWT) based lossy compression on the forecasting accuracy of three time series models (OLS, XGBoost, TiDE) for a smart grid case study of a seawater supply system in Hirtshals, Denmark. Compression is performed by thresholding wavelet coefficients, with the lossy compression rate defined as the fraction of zeroed coefficients. Five biorthogonal wavelets and rates up to 0.999 are considered, and Normalized Mutual Information (NMI) is used to quantify information retention. The results show that XGBoost is largely unaffected by compression up to r=0.99, while OLS is highly sensitive to smooth wavelets and high rates, and TiDE shows intermediate variability. The paper claims that wavelet compression can substantially reduce storage and transmission requirements without sacrificing forecasting accuracy.

Significance. If the claims hold, the paper offers a practically useful empirical result: robust forecasting models such as XGBoost can tolerate aggressive lossy wavelet compression, enabling data volume reduction in IoT-based smart energy systems. The study is clearly written, uses a real-world dataset, and systematically explores multiple wavelets and compression rates. The use of NMI as a task-agnostic information-retention measure is a sensible idea, and the observation of XGBoost's robustness is potentially valuable. However, the central quantitative claims are not yet validated because the evaluation protocol measures distribution-shift robustness rather than the deployment compression tradeoff, and the compression-rate metric is a sparsity fraction rather than an actual storage saving. With these issues addressed, the paper could be a solid applied contribution.

major comments (3)

[Section 3.2] The evaluation protocol trains and validates all models on lossy-compressed data but tests them on the corresponding uncompressed data. This is not the protocol a deployed edge-compression pipeline would use: at inference time, the inputs to the model would also be reconstructed from the lossy representation. As written, the experiments measure robustness to a train/test distribution shift, not the compression/forecasting tradeoff claimed in the abstract. The extreme OLS failures in Table 2 (e.g., bior6.8 at r=0.6, RMSE 6372.656) are largely a consequence of this mismatch, since the model learns smooth short-lag inputs and then receives noisy ones at test. The manuscript mentions that smoothing the test data could mitigate this but does not adopt that check, and no alternative protocol is reported. Please either add a deployment-consistent evaluation (e.g., testing on reconstructed data from the same compression pipeline) or re-frame the existing results as a distribution-shift robustness study.
[Section 2.2.2] The lossy compression rate r_lossy = N0/NY is defined as the fraction of wavelet coefficients that are zeroed after thresholding. This is not the actual storage reduction achieved: the retained non-zero coefficients and their positions must still be encoded, and the approximation coefficients at the coarsest decomposition level are always stored. As a result, a reported r_lossy of 0.99 does not imply a 100x reduction in file size, and the comparison in Section 3.2 with Brotli's r_lossless=0.36 (a file-size reduction) is apples-to-oranges. The central quantitative claims about achievable compression (abstract, Section 4) rest on this metric. Please report a true bitrate- or file-size-based compression ratio, or explicitly relabel r_lossy as a sparsity fraction and temper the storage-claim language accordingly.
[Sections 2.2.1-2.2.2] The manuscript does not specify how the threshold epsilon is selected to achieve each target r_lossy, nor the DWT decomposition depth used. These details determine the set of retained coefficients and are essential for reproducibility and for interpreting the differences between wavelets. Without them, the reported r_lossy values are underdetermined and the experiment cannot be replicated. Please state the threshold-selection rule (e.g., quantile of coefficient magnitudes) and the decomposition level, or provide the code that implements the compression pipeline.

minor comments (6)

[Section 3.2 / Table 2] Aggregate RMSE/MAE values are reported without confidence intervals or standard errors, despite strong variability across the 12 test datasets visible in Figure 4. Provide an uncertainty measure for the headline comparisons.
[Section 2.3] Model specifications (lag lengths p and q, XGBoost hyperparameters, TiDE architecture and training details) are not reported; if library defaults were used, state this explicitly.
[Section 2.2.3] The notation I(˜Y0;Y) in the NMI definition is confusing because Y and ˜Y0 both denote the original signal; clarify that the denominator is H(Y) when r=0.
[Section 3.3 / Figures 5-6] The x-axis is logit-scaled in Figure 5 but linear in Figure 6; use a consistent scale for easy comparison.
[Abstract / Table 2] The abstract's claim that XGBoost maintains stable performance across diverse compression rates is too strong given the large error increases at r=0.999 (e.g., bior1.5 RMSE 0.402 vs. 0.041 baseline); qualify the claim to 'up to r=0.99'.
[Section 3.3] The elbow-method recommendation is a heuristic based on the same data used to fit the beta curves and observe the RMSE-NMI relationship; it is not an independent, validated selection criterion. Consider presenting it as an observation or a hypothesis for future work.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the forecasting results are empirical measurements, and the NMI fit is descriptive rather than load-bearing.

full rationale

The paper's central claims—that wavelet-based lossy compression can preserve forecasting accuracy for robust models and that XGBoost is particularly robust—are empirical measurements on held-out test data, not derivations from a fitted parameter. The incomplete beta fit to NMI in Section 3.3 is explicitly descriptive: the paper fits NMI(r) = 1 − I_r(α, β) and reports the fitted curves, but it does not use this fit to construct the RMSE results or to generate the central claims. The recommended elbow method is presented as a heuristic for selecting compression rates, not as a prediction derived from the fitted curve, so there is no fitted-input-called-prediction circularity. The train-on-compressed/test-on-uncompressed protocol is a possible threat to external validity for the intended deployment, but it is an evaluation-protocol concern, not a circularity concern: nothing in the protocol makes the outcome equal to the input by construction. The paper also does not rely on any load-bearing self-citation or imported uniqueness theorem; its references to prior wavelet and forecasting work are standard background. Overall, the derivation chain is self-contained in the relevant sense: the reported RMSE/MAE values are direct empirical outcomes, and the NMI analysis is an accompanying diagnostic rather than a source of the central results. Therefore, no circular step meets the evidentiary bar required for a positive finding.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on standard wavelet mathematics plus several domain assumptions about the dataset and evaluation protocol. No new entities are introduced. The only fitted quantities are descriptive parameters for the NMI curves and the threshold epsilon. The most fragile premise is the train/test mismatch protocol, which strongly influences the OLS failure results.

free parameters (3)

Incomplete beta fit parameters (alpha, beta) per wavelet = bior1.1: (0.36, 0.13); bior1.5: (0.43, 0.17); bior2.8: (0.65, 0.22); bior3.9: (0.56, 0.21); bior6.8: (0.49, 0.19)
Fitted by least squares to the NMI curves in Section 3.3; used only descriptively for the elbow recommendation, not for prediction.
Wavelet coefficient threshold epsilon = implicitly tuned to hit each target r_lossy
The paper thresholds detail coefficients at |d| > eps but does not state how eps is computed to achieve the advertised N0/NY rates; this is a per-dataset tuning parameter.
k in k-NN mutual information estimator = 10
Choice of neighbor count for MI estimation, stated in Section 3.3; not varied.

assumptions (4)

standard math The DWT with biorthogonal wavelets provides perfect reconstruction and thresholding yields a valid sparse approximation of the original series.
Standard wavelet theory, cited via [25,26] in Section 2.2.1.
domain assumption The Hirtshals seawater dataset is representative of smart grid time series demand forecasting.
The paper generalizes from one 308-day dataset from a single seawater supply system to smart energy systems broadly (Sections 1 and 5).
domain assumption The chosen evaluation protocol (train on compressed, test on uncompressed) captures the operational scenario where historical data is stored compressed but new data arrives raw.
Section 3.2 states models are trained and validated on compressed data and tested on uncompressed data; the realism of this mismatch is asserted, not justified.
domain assumption The k-nearest-neighbor estimator with k=10 provides accurate mutual information estimates for the NMI curves.
Section 3.3 uses k-NN MI; accuracy of this estimate on the data is not validated.

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Pith. "Pith review of Data Compression for Time Series Modelling: A Case Study of Smart Grid Demand Forecasting." pith.science (2026). https://pith.science/paper/RY6RHFE7

@misc{pith2026250502606,
  author       = {Pith},
  title        = {Pith review of: Data Compression for Time Series Modelling: A Case Study of Smart Grid Demand Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RY6RHFE7}},
  note         = {Machine review of arXiv:2505.02606}
}

abstract

Efficient time series forecasting is essential for smart energy systems, enabling accurate predictions of energy demand, renewable resource availability, and grid stability. However, the growing volume of high-frequency data from sensors and IoT devices poses challenges for storage and transmission. This study explores Discrete Wavelet Transform (DWT)-based data compression as a solution to these challenges while ensuring forecasting accuracy. A case study of a seawater supply system in Hirtshals, Denmark, operating under dynamic weather, operational schedules, and seasonal trends, is used for evaluation. Biorthogonal wavelets of varying orders were applied to compress data at different rates. Three forecasting models - Ordinary Least Squares (OLS), XGBoost, and the Time Series Dense Encoder (TiDE) - were tested to assess the impact of compression on forecasting performance. Lossy compression rates up to $r_{\mathrm{lossy}} = 0.999$ were analyzed, with the Normalized Mutual Information (NMI) metric quantifying the relationship between compression and information retention. Results indicate that wavelet-based compression can retain essential features for accurate forecasting when applied carefully. XGBoost proved highly robust to compression artifacts, maintaining stable performance across diverse compression rates. In contrast, OLS demonstrated sensitivity to smooth wavelets and high compression rates, while TiDE showed some variability but remained competitive. This study highlights the potential of wavelet-based compression for scalable, efficient data management in smart energy systems without sacrificing forecasting accuracy. The findings are relevant to other fields requiring high-frequency time series forecasting, including climate modeling, water supply systems, and industrial operations.

Figures

Figures reproduced from arXiv: 2505.02606 by the authors.

**Figure 2.** Example of model predictions for all 3 time series forecasting models. Each model used a context of six hours [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Example subset of the compressed, normalized target variable. The rows show different compression rates [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: RMSE for every model against the compression rate [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 5.** Figure 5: Normalized Mutual Information (NMI) for each wavelet as the compression is increased. Note that the x-axis [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 6.** Figure 6: Normalized Mutual Information (NMI) for each wavelet as the compression is increased, with regularized, [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

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