Corrected Support Vector Regression for intraday point forecasting of prices in the continuous power market

Andrzej Pu\'c; Joanna Janczura

REVIEW 2 major objections 6 minor 52 references

Corrected Support Vector Regression for intraday point forecasting of prices in the continuous power market

T0 review · 2 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Corrected SVR, which folds the naive price forecast into its kernel, beats plain SVR, LASSO, Random Forest and the naive benchmark for very short-term German intraday power prices while running faster than the machine-learning rivals.

desk verdict Useful empirical adaptation of a kernel-correction idea to intraday power price forecasting, with a solid but small accuracy gain; the NTK story needs an ablation before it is the headline. read the letter →

arxiv 2411.16237 v1 pith:P43DE6YS submitted 2024-11-25 stat.AP

Andrzej Puć , Joanna Janczura This is my paper · ORCID

classification stat.AP MSC 62M2062G0868T05

keywords electricitypriceforecastingintradaycontinuousmarketsupportvectorregressionkernelmethodsnaiveforecastaveragingGermanpoint

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 claims a simple kernel-level change makes Support Vector Regression the best fast forecaster for very short-term continuous intraday electricity prices. Instead of treating the last known price only as a predictor or a benchmark, the authors multiply the SVR's Laplace kernel by a Gaussian kernel built on that naive forecast, calling the result corrected SVR (cSVR). On German 15-minute intraday data the weighted-averaged cSVR beats plain SVR, LASSO, Random Forest and the naive benchmark in accuracy while being the fastest of the machine-learning models. The largest gains occur in morning and evening peak hours, where the naive forecast is weakest and liquidity is highest. If the claim holds, cSVR offers a practical, computationally cheap tool for intraday trading signals in continuous power markets.

What carries the argument

The central object is the corrected kernel of Eq. (12): $K^i(x,x') = \exp(-l^i \|x-x'\|_2^2)\cdot \exp(-g|\tilde{P}_t - \tilde{P}_{t'}|^2)$. The first factor is the Laplace kernel with L2 distance (instead of the classical L1); the second is a Gaussian kernel whose input is the standardized naive forecast. The product acts as a data-dependent weight: training days whose last-known prices are far from the current day get down-weighted in the SVR expansion, importing the 'local elasticity' idea from label-aware neural tangent kernels into time-series forecasting. The kernel widths are set from empirical quantiles of pairwise distance matrices, avoiding cross-validation. This corrected kernel is the load-bearing piece that separates cSVR from plain SVR.

What would settle it

A reader could settle the claim by re-running the study with the Gaussian correction factor replaced by a constant, i.e., plain L2-Laplace SVR on the same expert variable sets and hyperparameters: if the reported roughly 2-3 percentage-point rMAE advantage of cSVR at 60-minute lead time does not shrink or reverse, the kernel correction is not the active ingredient.

Watch

Extended reading notes

Core claim

The paper's central claim is that a Support Vector Regression whose kernel is multiplied by a Gaussian built on the standardized naive forecast delivers the most accurate very short-term point forecasts of continuous intraday electricity prices among the models tested, and does so at the lowest computational cost. Tested on German 15-minute products across 2020, the weighted-averaged cSVR outperforms plain SVR, LASSO, Random Forest and the naive benchmark, with the largest gains concentrated in morning and evening peak deliveries. At 60-minute lead time and averaged over horizons and deliveries, cSVR's MAE is roughly 3% below the naive forecast, while the best LASSO variant gains only about 0.5%, and plain SVR and Random Forest on average do not beat the naive. The authors attribute this to the kernel correction: by down-weighting pairs of training days whose naive forecasts are far apart, the model reduces the influence of uninformative historical samples. The result matters because very short-term intraday price forecasting has previously been dominated by the naive benchmark, and cSVR is the fastest model in the comparison.

Load-bearing premise

The load-bearing premise is that multiplying the Laplace kernel by a Gaussian built on the standardized naive forecast transfers the label-aware kernel-correction effect from classification to time-series regression, so that down-weighting training days with distant naive forecasts improves out-of-sample accuracy.

Editorial extensions

If this is right

For a 60-minute lead time, the weighted-averaged cSVR cuts MAE by about 2.9% relative to the naive forecast, while the strongest LASSO variant improves by only about 0.5% and plain SVR and Random Forest on average do not beat the naive.
The largest gains are in morning and evening peak deliveries, where cSVR beats the naive by more than 5% for many horizon-delivery combinations and by up to 15.5% for the 17:45 delivery at a 480-minute horizon.
cSVR is the fastest model in the study; LASSO is faster only for very early deliveries and Random Forest is slower in every configuration.
Using the L2 norm in the Laplace kernel outperforms the classical L1 version, and the best single expert variable set combines exogenous fundamentals with only the most recent price information.
In Diebold-Mariano tests at the 5% level, cSVR is significantly better than the naive for all forecasting horizons in 79 of 576 delivery-lead-time aggregations, concentrated in morning, evening, and early-night hours.

Reading between the lines

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

We infer that the same multiplicative kernel correction could work with other base kernels and other auxiliary forecasts, such as day-ahead or auction prices, whenever the auxiliary series is informative about the target; the paper itself only tests the naive forecast as the correction input.
We infer that the benefit of the correction will shrink in regimes where the naive forecast is weak, such as very illiquid deliveries or price-spike days, because the Gaussian factor then down-weights training days on the basis of a signal that carries little information.
A testable extension suggested by the mechanism is to apply the correction to probabilistic or quantile forecasts: because the kernel operates on response-linked distances before any distributional layer, it could sharpen prediction intervals in volatile peak hours without retraining the point forecaster.

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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

Dear Colleague,

Bottom line: this is a useful applied paper with a real but narrower contribution than its NTK narrative suggests. It takes the label-aware kernel idea from Chen et al. (2020) and applies it to SVR for intraday electricity price forecasting: multiply the Laplace kernel by a Gaussian kernel on the standardized naive forecast. On the German continuous intraday market, the weighted average of three cSVR variants beats the naive benchmark by roughly 3% MAE, and also beats plain SVR, LASSO, and RF over the 2020 test period, while being computationally fast. The study is large (year-long OOS, many horizons, lead times, deliveries, DM tests) and the authors are honest about hand-picked hyperparameters.

What is actually new: the first time-series application of this kernel correction construction, and the quantile-based rule for kernel widths is a sensible practical choice. The empirical comparison is credible as far as it goes. The citation pattern looks appropriate: prior intraday forecasting work, NTK, and local elasticity citations are all in place.

Soft spots, in order. First, the mechanism story is not isolated. For S1 and S3, which drive the averaged results, Eq. 12 is algebraically an anisotropic RBF kernel on features that already include the naive forecast. The K1 vs K4 comparison changes the kernel metric but does not establish a label-aware down-weighting effect. Without a permutation control (e.g., shuffling naive forecast values across training days), the NTK/local-elasticity interpretation remains a hypothesis. That does not kill the empirical claim, but it changes what the paper has actually shown.

Second, the gains are modest and concentrated in peak hours; midday performance is close to naive. And since the naive forecast is inside the averaging scheme, the comparison is partly stacked. Third, there is no code or data, and several hyperparameters are set without cross-validation. The authors acknowledge this, but it limits verification and the strength of the benchmark claim.

Who is this for: people working on very short-term electricity price forecasting, continuous intraday markets, and kernel methods. They will get a practical method and a clean empirical setup, with caveats.

Recommendation: send to peer review. A serious referee should ask for an ablation that isolates the role of the naive forecast and for released code/data before the paper is treated as a definitive benchmark.

Referee Report

2 major / 6 minor

Summary. This paper proposes 'corrected support vector regression' (cSVR) for point forecasting of quarter-hourly prices in the German continuous intraday power market. The method multiplies an L2-norm Laplace kernel by a Gaussian kernel built on the standardized naive forecast (Eq. 12), motivated as a label-aware correction inspired by neural tangent kernels and local elasticity. The authors evaluate cSVR on three expert feature sets, with simple and inverse-MAE-weighted forecast averaging that also includes the naive forecast, over a one-year out-of-sample window (2020), for ten forecasting horizons (30-480 minutes), six lead times (30-180 minutes), and all 96 quarter-hourly deliveries. Benchmarks are plain SVR (L1 and L2 norms), LASSO, Random Forest, and the naive forecast. The headline claims are that weighted-averaged cSVR achieves the highest forecast accuracy, with the largest gains for morning and evening peak deliveries, is computationally the fastest among the benchmarks, and is significantly more accurate than the naive forecast for a large proportion of delivery-lead-time-horizon combinations according to a Diebold-Mariano test.

Significance. The study's strengths are its scale, the careful handling of data-availability delays, and the authors' explicit disclosure of hand-picked hyperparameters. If the empirical results hold, cSVR is a useful addition to the intraday forecasting toolbox, particularly because it is competitive while being fast and because the kernel widths are set by data quantiles without cross-validation. The delivery-level resolution of the gains (Figure 15) and the DM-test evidence against the naive benchmark are the most convincing parts of the paper. However, the central methodological novelty claim is not supported by the experiments as designed: the product kernel in Eq. (12) is algebraically an anisotropic Gaussian/RBF kernel, and for feature sets S1 and S3 the naive forecast is already one of the input coordinates (Eqs. 3, 5, 11). The reported gains are therefore consistent with a more modest contribution, namely anisotropic kernel weighting plus ensemble averaging, and the label-aware narrative requires an additional control experiment before it can be accepted.

major comments (2)

[§3.1.1, Eq. (12); Eqs. (3), (5), (11); Fig. 14] The proposed kernel correction is not identifiable from the reported comparisons. Eq. (12) defines the corrected kernel as exp(-l ||x̃ - x̃'||²) · exp(-g ||P̃_naive - P̃_naive'||²), which equals exp(-l ||x̃ - x̃'||² - g ||P̃_naive - P̃_naive'||²). For the feature sets S1 and S3 (Eqs. 3 and 5), the naive forecast of Eq. (11) is, by construction, an explicit element of the feature vector x, namely the 'last known undifferentiated price' P_{d,T}(m-20). The product kernel is therefore an anisotropic RBF/Gaussian kernel on the same feature space, with an additional weight concentrated on one coordinate; it is not a separate mechanism of the kind the paper describes. Because the comparison between K1 and K4 in Figure 14 changes the kernel metric (isotropic versus anisotropic weighting) as well as the interpretation, the reported improvement does not isolate a label-aware down-weighting effect. The paper should add a control that breaks the link between the correction factor and the response, for example permuting the naive-forecast values across training days (or replacing the naive coordinate with a non-informative one) and checking whether the out-of-sample gain persists. Without such a control, the central novelty claim in Section 5 ('first direct implementation of this idea in time series forecasting') is not established.
[§4.1, Figs. 16-18; Table 2] The top-line claim that cSVR with averaging 'yields the highest forecast accuracy' among the considered benchmarks rests on point estimates only. The one-sided Diebold-Mariano test is applied exclusively to the comparison of cSVR with the naive forecast, while the comparisons against plain SVR, LASSO, and Random Forest are reported as rMAE differences without significance testing. Given the reported margin against the best alternative benchmark (cSVR w.avg rMAE of -2.9% versus -0.5% for LASSO w.avg in Table 2, averaged over horizons), pairwise DM tests between cSVR and the best competing model would directly support the abstract's claim. With the evidence as presented, 'highest forecast accuracy' is a statement about point estimates rather than about statistically detectable superiority.

minor comments (6)

[Abstract; Table 3] The claim that cSVR is 'the fastest from the considered benchmarks' is not valid for the earliest deliveries: in Table 3, for delivery 1, LASSO is faster than cSVR for all three reported lead times (e.g., 204.88 s versus 302.85 s at lead time 30). The body of Section 4.1 qualifies this correctly, so the abstract should be rephrased accordingly.
[§2.2, Eqs. (2)-(3)] The set notation in Eq. (2) is typeset incorrectly (a stray arrow and garbled floor expressions), and Eq. (3) contains 'ˆui =∈ ˆu' instead of 'ˆui ∈ ˆu'; these should be corrected.
[§3.1.1, Eqs. (13)-(14)] The kernel in Eq. (13) is called a Laplace kernel but uses the L2 norm, which makes it the Gaussian/RBF kernel; the terminology should be clarified to avoid confusion, since the L2 choice is justified only empirically in Figure 14.
[§3.1, §3.3, §5] The hyperparameters C=1, epsilon=0.1, the correlation thresholds (0.8 for S1, 0.95 for S2), the kernel-width quantile (0.75), the Random Forest size (256 trees, depth 8), and the averaging calibration window (W=7) are all fixed by hand. The authors disclose this in Section 5, but a small sensitivity analysis for the SVR hyperparameters and for W on a subset of cells would demonstrate that the reported model ordering is not an artifact of these choices.
[§4, test window] The out-of-sample evaluation covers a single year (2020), which includes the COVID-19 price and load patterns; a brief discussion of the representativeness of this test year and the robustness of the conclusions across years would strengthen the generalization claims.
[End matter] No data or code availability statement is provided; making the code available, even in part, would substantially increase the reproducibility of the study.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the cSVR accuracy claim is an empirical out-of-sample comparison, and no prediction reduces to a fitted parameter by construction.

full rationale

The paper's central claim is the out-of-sample forecast accuracy of cSVR against benchmarks. No target-day value enters model fitting: kernel widths are computed from training-window quantiles (Eqs. 17-20), the SVR parameters solve a penalized regression on training days, and the averaging weights are calibrated on a rolling seven-day window preceding each forecast day (Section 4). Thus no fitted input is renamed a prediction. The product kernel in Eq. (12) is algebraically equivalent to an RBF kernel on a feature vector in which the naive forecast coordinate receives extra weight; for sets S1 and S3 the naive forecast P_{d,T}(m-20) is already an element of the feature vector (Eqs. 3 and 5), so the comparison of K1/K3 with K4 varies both the kernel family and the metric and does not isolate the label-aware mechanism. This is a potential confound in attributing the improvement, but it is not a circularity: the reported MAE gains are empirical and are not guaranteed by the construction. The only self-citation, [27], supports a descriptive statement about residual-load price patterns and is not load-bearing. The paper also openly acknowledges hand-picked hyperparameters and the lack of cross-validation (Sections 3.3 and 5), which are correctness and robustness limitations rather than circular steps.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central claim rests on standard kernel regression theory, the domain-specific assumption that the naive forecast is a useful label for kernel correction, and a set of hand-picked hyperparameters. No new physical or formal entities are introduced. The free parameters are all choices made by the authors, not outputs of a derivation.

free parameters (6)

SVR cost C = 1
Chosen arbitrarily in Section 3.1; authors acknowledge cross-validation should be performed.
SVR epsilon = 0.1
Chosen arbitrarily in Section 3.1.
Kernel width quantile p = 0.75
Arbitrary quantile used in Eqs. (17) and (20) to set Laplace and Gaussian kernel widths.
Correlation filter thresholds = 0.8 (S1), 0.95 (S2)
Arbitrary thresholds in Section 2.3 for dropping highly correlated variables.
Random Forest hyperparameters = n_estimators=256, max_depth=8
Arbitrary trade-off between accuracy and compute; acknowledged in Section 3.3.
Averaging weight calibration window W = 7 days
Rolling out-of-sample window used to set weights in Eq. (25); choice not justified beyond prior literature.

assumptions (6)

standard math SVR dual formulation and representer theorem are valid for the kernels used.
Section 3.1 relies on standard kernel regression theory.
standard math Kernels defined in Eqs. (12)-(14) are positive semidefinite and yield valid SVR solutions.
Products of positive definite kernels (Laplace, Gaussian) are positive definite; the paper does not prove this but it is standard.
domain assumption Data availability delays: ENTSO-E data delayed 60 minutes, EPEX continuous prices delayed 20 minutes.
Section 2.2 assumes these publication lags; if actual lags differ, the feature timing is wrong.
domain assumption Preprocessing: minutes without trades are filled with the auction intraday price, and trajectories after delivery are extended with the 3-hour average price.
Section 2.1; these choices affect the training features and could bias results.
domain assumption The naive forecast (last known price) is a strong and appropriate auxiliary variable for kernel correction and forecast averaging.
Section 3.1.1 and 4; this is the core modeling premise of cSVR.
domain assumption The 2020 test year is sufficiently representative; expanding-window training from 2018-2019 generalizes despite the COVID-19 regime shift.
Section 4; the model is evaluated on a year with unusual market conditions.

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Cite this review

Pith. "Pith review of Corrected Support Vector Regression for intraday point forecasting of prices in the continuous power market." pith.science (2026). https://pith.science/paper/P43DE6YS

@misc{pith2026241116237,
  author       = {Pith},
  title        = {Pith review of: Corrected Support Vector Regression for intraday point forecasting of prices in the continuous power market},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P43DE6YS}},
  note         = {Machine review of arXiv:2411.16237}
}

read the original abstract

In this paper, we develop a new approach to the very short-term point forecasting of electricity prices in the continuous market. It is based on the Support Vector Regression with a kernel correction built on additional forecast of dependent variable. We test the proposed approach on a dataset from the German intraday continuous market and compare its forecast accuracy with several benchmarks: classic SVR, the LASSO model, Random Forest and the na\"{i}ve forecast. The analysis is performed for different forecasting horizons, deliveries, and lead times. We train the models on three expert sets of explanatory variables and apply the forecast averaging schemes. Overall, the proposed cSVR approach with the averaging scheme yields the highest forecast accuracy, being at the same time the fastest from the considered benchmarks. The highest improvement in forecast accuracy is obtained for deliveries in the morning and evening peaks.

Figures

Figures reproduced from arXiv: 2411.16237 by the authors.

**Figure 1.** Price averages over the whole dataset and 30 minutes intervals of transaction time. The averages were separately [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

**Figure 2.** Standard deviation of transaction prices in one minute averaged over 30 minutes intervals of transaction time and the [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Total number of transactions in every 30 minutes trade time interval. The number of transactions were separately [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (15 more)

**Figure 4.** Figure 4: Prices trajectories for chosen Monday, 03.02.2020, deliveries. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: Exogenous variables, i.e. cross-border physical flow between France and Germany (top panel); RES generation and [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: Top panel: auction intraday, continuous intraday and day-ahead averaged electricity prices for all 96 quarter-hourly [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 7.** Figure 7: Sample transaction prices for quarter-hourly deliveries on 11-03-2019 starting at 7:00, 10:00, 15:00, 19:00 (left panel) [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

**Figure 8.** Figure 8: Sample transaction volumes for quarter-hourly deliveries on 11-03-2019 starting at 7:00, 10:00, 15:00, 19:00 (left [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

**Figure 9.** Figure 9: Forecasting task timeline. Delivery quarter hour is denoted as [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]

**Figure 10.** Figure 10: Timeline of data availability for all exogenous variables used in the study. Time moments indicating when the data [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]

**Figure 11.** Figure 11: Percentage of variables rejected by the correlation filter in set [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]

**Figure 12.** Figure 12: Kernels with quantile dependent widths, (17), (19). [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]

**Figure 13.** Figure 13: Flowchart of the forecast calculation for each of the considered models. Note that, for clarity, the indexes are [PITH_FULL_IMAGE:figures/full_fig_p019_13.png]

**Figure 14.** Figure 14: Relative errors, rMAEmodelvariant m,s obtained for forecasts calculated using different approaches: cSVR calculated for individual variables sets cSVRi , i = 1, 2, 3; averaged cSVR, cSVRavg. and cSVRw.avg.; SVR with L1 and L2 norm, SVR4 and SVR5 ; weighted averages of…

**Figure 15.** Figure 15: Relative MAE, (27), for the cSVR model forecasts averaged as in (25) and lead time of 60 minutes. Deliveries for [PITH_FULL_IMAGE:figures/full_fig_p022_15.png]

**Figure 16.** Figure 16: MAE of the cSVR model with forecast averaging (25) (top panel, solid lines) and MAE of the naïve forecast (top [PITH_FULL_IMAGE:figures/full_fig_p023_16.png]

**Figure 17.** Figure 17: Proportion of the forecast horizons for which the weighted averaged cSVR model forecasts were significantly more [PITH_FULL_IMAGE:figures/full_fig_p024_17.png]

**Figure 18.** Figure 18: Proportion of the DM test null hypothesis rejections in forecasting horizons, averaged over the lead times, see also [PITH_FULL_IMAGE:figures/full_fig_p024_18.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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