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REVIEW 4 major objections 5 minor 52 references

A Comparison of High-Dimensional Variable Selection Procedures for Electricity Spot Price Forecasting

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Boosting with Multiple Testing, a one-variable-at-a-time selection method, matches the out-of-sample forecast accuracy of LASSO and Elastic Net in six European electricity markets while selecting fewer than one-tenth as many variables.

desk verdict Solid six-market comparison; BMT's parsimony is real, but tuning asymmetry and an overreaching abstract keep the headline claim from being as clean as it looks. read the letter →

arxiv 2608.09213 v1 pith:RH2L3DK5 submitted 2026-08-10 econ.EM

Charisios Grivas , Mikkel Mandrup , Orimar Sauri This is my paper · ORCID
classification econ.EM
keywords electricitypriceforecastingvariableselectionLASSOElasticNetBoostingwithMultipleTestingmodelparsimonyDiebold-Marianotest
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 sets out to establish that a multiple-testing variable-selection algorithm called Boosting with Multiple Testing (BMT) can forecast day-ahead electricity spot prices as accurately as the shrinkage benchmarks LASSO and Elastic Net, while keeping far fewer variables in the model. Using rolling-window forecasts over four out-of-sample years in six European price areas, the authors find that BMT selects on average 4.5 to 8.2 covariates per market, against roughly 88 to 133 for the penalized methods, and that Diebold–Mariano tests find its accuracy statistically indistinguishable from or better than theirs in most markets. The authors conclude that the over-parameterized models produced by regularization methods are not a necessary price for predictive accuracy in electricity price forecasting.

What carries the argument

The load-bearing object is the BMT selection rule: at each stage every remaining candidate is tested individually conditional on the variables already chosen, using the OCMT critical value $c_p(d,\delta)=\Phi^{-1}\left(1-\frac{p}{2 f(d,\delta)}\right)$, and only the candidate with the largest absolute $t$-statistic among those passing the threshold is admitted. The one-at-a-time admission is what separates BMT from OCMT and GOCMT, which admit every variable passing the filter; it is designed to stop pseudo-signals, covariates correlated with true signals but with zero coefficients, from entering the model once the true signal is conditioned on. The rest of the comparison setup, 24 separate hourly equations, 562 candidate variables, a 731-day rolling window, and Diebold–Mariano tests, is the standard frame in which BMT's parsimony is measured against the shrinkage baselines.

What would settle it

Run a synthetic null experiment with the same 562 candidate variables and the same correlation structure as the real electricity data, but with all regression coefficients equal to zero, and apply BMT with $p=0.05$, $\delta_1=\delta_2=1$. If BMT selects a substantial number of variables on average in such data, the borrowed OCMT critical value does not control type-I error for the one-at-a-time rule, and the parsimony-accuracy comparison would not be a stable property of the method.

Watch

Extended reading notes

Core claim

The central claim is that BMT delivers out-of-sample forecasting performance statistically comparable to Elastic Net and LASSO while using less than one-tenth as many variables. On hourly forecasts BMT and Elastic Net trade the lowest evaluation metrics across markets, and on daily baseload forecasts BMT has the lowest MAE, RMSE, sMAPE, and rMAE in five of six price areas. BMT's average model size ranges from about 4.5 to 8.2 variables, compared with roughly 88 to 133 for LASSO and Elastic Net, making the shrinkage specifications 10 to 20 times larger. The same comparisons show FarmSelect, OCMT, and GOCMT underperforming the top three methods, so the paper's conclusion is that parsimonious multiple testing, rather than regularization, is the better operating point in this setting.

Load-bearing premise

The load-bearing premise is that the OCMT critical-value formula still controls false discoveries when BMT keeps only the single largest $t$-statistic at each step; the paper does not provide a proof or null simulation for this sequential-maximum rule, so if the threshold is miscalibrated, BMT could be selecting too many or too few variables and the parsimony result would be an artifact.

Editorial extensions

If this is right

  • For day-ahead price forecasting in the six markets studied, BMT can replace LASSO or Elastic Net with no statistically significant loss in accuracy and a model that is an order of magnitude smaller.
  • BMT's per-day recalibration takes 1–3 seconds versus 15–127 seconds for the shrinkage methods, so repeated backtests that take the penalized methods hours or days can be run in minutes.
  • The failure of OCMT and GOCMT, which pass all significant variables, to match BMT indicates that the one-at-a-time admission rule, rather than multiple testing per se, is what delivers the parsimony.
  • In the Nordic markets BMT is the best or tied-best method on all metrics, which suggests the advantage is not limited to one market structure.
  • The over-parameterization of LASSO and Elastic Net in this setting does not buy additional forecast accuracy, so practitioners can prefer smaller models without a penalty trade-off.

Reading between the lines

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

  • A direct testable extension would be to add dozens of noise variables strongly correlated with the price lags and check whether BMT's model size stays flat while LASSO and Elastic Net swell; the paper's mechanism predicts it would.
  • Because BMT's critical value is borrowed from OCMT, a null simulation study with all coefficients zero is the quickest way to check whether the stopping rule's false-positive rate is actually controlled; the paper does not report one.
  • If the stopping-rule concern is set aside, the same one-at-a-time selection could be lifted to probabilistic forecasting by selecting on the basis of a scoring rule rather than squared error, which is not explored here.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper compares six high-dimensional variable selection procedures for day-ahead electricity spot price forecasting: LASSO, Elastic Net, FarmSelect, OCMT, GOCMT, and the recently proposed Boosting with Multiple Testing (BMT). The empirical design uses hourly day-ahead prices and day-ahead forecasts of load and renewable generation from six European price areas, with a 731-day rolling window, 24 separate hourly equations, and 562 candidate variables per hour. Out-of-sample performance is evaluated over 2022–2025 using MAE, RMSE, sMAPE, rMAE, and multivariate and univariate Diebold–Mariano tests, with daily baseload forecasts and computational timings also reported. The central claim is that BMT matches the accuracy of LASSO and Elastic Net while using less than one-tenth as many variables, and that the over-parameterization typically associated with regularization methods is therefore not a necessary price for predictive accuracy in electricity price forecasting.

Significance. If the central claim held in full, the paper would make a practically useful contribution to the electricity price forecasting literature by showing that highly parsimonious multiple-testing-based selection can match shrinkage methods in accuracy. The paper is valuable in bringing BMT and related methods to an EPF setting and in providing a transparent multi-market, rolling-window benchmark with formal equal-accuracy tests. The empirical work is extensive: six markets, four years of out-of-sample evaluation, both hourly and daily baseload forecasts, and explicit computational-time comparisons. However, the headline claim is overstated relative to the evidence in France, and the parsimony advantage of BMT is partly confounded by the asymmetric tuning of the competing methods. The manuscript's conclusion therefore needs substantial qualification and additional benchmarks before the central claim can be accepted.

major comments (4)
  1. [Section 4.2 and Table 4.1] The abstract's claim that BMT matches LASSO and Elastic Net 'without any loss of forecasting accuracy' is contradicted by the France results. In the multivariate DM test, Elastic Net is significantly more accurate than every other method at the 5% level, and LASSO outperforms BMT at the 10% level. Table 4.1 confirms the direction of the difference: in France, EN has rMAE 0.470 versus BMT 0.497, MAE 18.840 versus 19.936, and RMSE 32.457 versus 34.056. The conclusion should be qualified as holding in most markets, or as statistical indistinguishability in five of six markets, rather than as 'without any loss of forecasting accuracy.'
  2. [Section 4 (implementation settings) and Section 5] The parsimony comparison is confounded by asymmetric tuning of the methods. LASSO and FarmSelect select the regularization parameter via LARS-AIC, and Elastic Net via an AIC grid search, while BMT uses the fixed, very stringent settings p=0.05, c=1, delta1=delta2=1; with d=562, the Stage-1 threshold in Eq. (3.4) is approximately Phi^{-1}(1 - 0.05/(2*562)) ≈ 3.40. AIC is known to retain many predictors in highly correlated settings, so the 10-to-20-fold difference in #vars reported in Table 4.1 may reflect the tuning rule rather than an intrinsic property of BMT. To support the conclusion that 'over-parameterization ... is not a necessary price,' the authors should add benchmarks with sparser tuning of LASSO and Elastic Net, such as BIC or one-standard-error cross-validation, and show that BMT retains its parsimony advantage under those alternatives.
  3. [Section 3.3 and Eq. (3.4)] The validity of BMT's stopping rule is not established. BMT inherits the OCMT critical value function c_p(d,delta) from Eq. (3.4), but its selection rule differs from OCMT: at each stage only the single largest t-statistic is admitted, and Stage 1 appears to select the maximum t-statistic unconditionally, without applying c_p. The null distribution of this sequential maximum is not the same as the distribution for the OCMT all-pass rule, so family-wise error control cannot simply be assumed from Chudik et al. (2018). The paper should either provide a theorem or a precise citation to a theorem in Kapetanios et al. (2026) or Grivas et al. (2026) covering this rule, or report simulations of BMT's selection behavior under the null. Without this, the parsimony finding could be an artifact of an invalid or miscalibrated stopping rule.
  4. [References and Section 3.3] The manuscript does not disclose that the first author is a co-author of the two BMT papers (Kapetanios et al., 2026; Grivas et al., 2026) and that the BMT implementation settings used in Section 4 were chosen by the method's own developers. This is not an accusation of bias, but it is material context for interpreting the favorable BMT results, and the paper should state the overlap explicitly in the introduction or methodology section.
minor comments (5)
  1. [Abstract] The abstract contains a stray hyphen in 'ac-curacy' from a line break; also, the manuscript inconsistently writes 'day-ahead' and 'day ahead' in several places.
  2. [Section 2] In the paragraph on daylight-saving time, the sentence 'Wetransformdaysaffectedbydaylight-savingstotimecontain24observations' is missing spaces between words and should be rewritten as a complete sentence.
  3. [Eq. (3.4)] The definition of f(d,delta) in Eq. (3.4) mixes delta and delta1: the text writes f(d,delta) = c d^{delta1}, which is notationally inconsistent. Use delta1 throughout, or define f with a single argument that is then specialized to delta1 and delta2.
  4. [Section 4.2] The univariate Diebold-Mariano tests are applied at the 5% level to each of the 24 hours separately, without any adjustment for multiple testing. The authors should either report whether the main conclusions survive a simple Bonferroni or Benjamini-Hochberg correction across the 24 hours, or justify the unadjusted procedure.
  5. [Data availability] The manuscript does not include a data and code availability statement. Given the practical emphasis on reproducibility and computation time, I recommend adding one.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claim rests on an out-of-sample empirical comparison, not on fitted inputs or a self-citation chain.

full rationale

The paper's headline result—that BMT matches LASSO/Elastic Net forecasting accuracy while selecting far fewer variables—is an empirical outcome generated by rolling-window forecasts across six markets, with accuracy assessed by MAE, RMSE, sMAPE, rMAE, and Diebold–Mariano tests. No parameter is fitted to the out-of-sample data and then renamed a prediction; BMT's threshold settings (p=0.05, c=1, delta1=delta2=1) are fixed a priori and reported in Section 4. The only self-citation is the attribution of BMT to Kapetanios et al. (2026) and Grivas et al. (2026), but the procedure is fully specified in Section 3.3 using the OCMT critical value in Eq. (3.4), so the paper does not depend on the cited papers for the content of the empirical claim. The skeptical concern that LASSO and Elastic Net are tuned by AIC while BMT uses a fixed stringent threshold is a legitimate question about comparability of implementations, but it is not a circular reduction: the parsimony difference is a method-and-data outcome, and the accuracy equivalence is an out-of-sample finding that could have failed. No equation or fitted value in the paper is equivalent by construction to the conclusion.

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

No parameters were fitted to make the central claim work; all method hyperparameters (c=1, p=0.05, delta values, factor count criterion) are taken from prior literature. The main assumptions are the linear sparse DGP, validity of the multiple testing critical values for BMT's sequential max-t selection, and weak stationarity of the DM loss differential.

assumptions (4)
  • domain assumption Linear sparse DGP: y_t = beta_0 + sum_i 1(beta_i != 0) beta_i x_{t,i} + epsilon_t (Eq. 3.2).
    All six variable selection methods treat the forecasting problem as linear regression with a subset of true signals.
  • domain assumption Validity of the OCMT/BMT multiple testing critical values c_p(d, delta) under sequential selection.
    The paper borrows the critical value function from Chudik et al. (2018) and applies it to BMT's max-t rule; the distributional validity for that rule is not demonstrated here (Section 3.3, Eq. 3.4).
  • domain assumption Weak stationarity of the DM loss differential series.
    Stated in Section 4.2 as a requirement for the Diebold-Mariano test.
  • domain assumption Approximate factor model for FarmSelect and GOCMT.
    Appendix A.3 assumes candidate covariates follow X = F B' + U with a small number of latent factors.

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Cite this review

Pith. "Pith review of A Comparison of High-Dimensional Variable Selection Procedures for Electricity Spot Price Forecasting." pith.science (2026). https://pith.science/paper/RH2L3DK5

@misc{pith2026260809213,
  author       = {Pith},
  title        = {Pith review of: A Comparison of High-Dimensional Variable Selection Procedures for Electricity Spot Price Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RH2L3DK5}},
  note         = {Machine review of arXiv:2608.09213}
}
read the original abstract

The paper considers the problem of variable selection for forecasting electricity spot prices. High-dimensional methods such as LASSO and Elastic Net are widely used for this purpose, and while they exhibit strong predictive performance, their tendency to select over-parameterized models raises questions about interpretability. We evaluate the performance of six variable selection procedures, includingthe recently proposed Boosting Multiple Testing (BMT) method, using an extensive dataset from six regional electricity markets. We assess their performance in terms of both out-of-sample forecasting ac-curacy and model parsimony. We find that, although LASSO and Elastic Net achieve similar accuracy and outperform most screening alternatives, BMT matches their forecasting performance while using less than one-tenth as many variables. Our results reveal that BMT offers researchers and practitioners a substantially more interpretable and computationally efficient alternative to shrinkage methods, without any loss of forecasting accuracy. These findings suggest that the over-parameterization typically associated with regularization methods is not a necessary price for predictive accuracy in electricity price forecasting.

Figures

Figures reproduced from arXiv: 2608.09213 by the authors.

Figure 2.1
Figure 2.1. Day-ahead prices for the six considered price areas. [PITH_FULL_IMAGE:figures/full_fig_p006_2_1.png] view at source ↗
Figure 2.2
Figure 2.2. Preprocessed day-ahead prices for the six considered price areas using the area hyperbolic sine transformation. [PITH_FULL_IMAGE:figures/full_fig_p007_2_2.png] view at source ↗
Figure 4.1
Figure 4.1. Boxplot of hourly absolute error for BMT and Elastic Net. [PITH_FULL_IMAGE:figures/full_fig_p015_4_1.png] view at source ↗
Figures from the paper (3 more)
Figure 4.2
Figure 4.2. Figure 4.2: Heat map of the percentage of selected number of variables for each method from the groups Price lags, Load, [PITH_FULL_IMAGE:figures/full_fig_p017_4_2.png]
Figure 4.3
Figure 4.3. Figure 4.3: Results of multivariate DM test using the [PITH_FULL_IMAGE:figures/full_fig_p021_4_3.png]
Figure 4.4
Figure 4.4. Figure 4.4: Results of univariate DM test at a 5% level using the [PITH_FULL_IMAGE:figures/full_fig_p022_4_4.png]

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.