{"id":"9497c590-aba4-476b-80f3-7f0ed738c6bd","arxiv_id":"2608.09213","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"In a four-year out-of-sample comparison across six European power markets, BMT matches LASSO and Elastic Net forecast accuracy while selecting roughly 90% fewer variables.","lead":"This paper tests six variable-selection methods for forecasting electricity spot prices in six European markets. It finds that Boosting Multiple Testing, a little-used screening method, matches the accuracy of LASSO and Elastic Net while keeping models ten times smaller.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'less than one-tenth variables' comparison is confounded by tuning asymmetry: LASSO and Elastic Net are tuned by accuracy-oriented AIC, while BMT uses a fixed, very stringent multiple-testing threshold, so the parsimony claim may reflect tuning choices rather than a property of BMT.","rationale":"I read the paper as an empirical comparison whose central claim is the joint achievement of accuracy and parsimony by BMT, with the broader message that over-parameterization of regularization methods is not a necessary price. The weakest point is not the BMT stopping rule identified by the reader: since BMT continues iff the maximum absolute t-statistic exceeds the OCMT threshold, the stopping event matches the all-pass rule's threshold event, so the stage-wise false-positive probability is essentially the same; the conditional-distribution concern is a theoretical nuance but does not directly bear on the observed out-of-sample forecasts. The French exception is a genuine overstatement in the abstract, but it is already acknowledged in the body and is fixable by qualification; it does not threaten the five-market finding. The tuning asymmetry is more fundamental: the sparsity gap is partly manufactured by choosing AIC for shrinkage methods and a very high fixed threshold for BMT. A single robustness run with BIC or cross-validation would settle whether the 'over-parameterization is unnecessary' message is a property of BMT or of the tuning choices. The paper's detailed rolling-window evaluation, DM tests, and full reporting are strengths; the concern is about the interpretation, not the data work. Therefore the reader's CONDITIONAL verdict remains appropriate, though I would emphasize this additional required check.","tokens_in":24471,"tokens_out":16332,"duration_ms":154387,"concrete_test":"Rerun the same six-market rolling-window design with LASSO and Elastic Net tuned by (i) BIC and (ii) 10-fold cross-validation with the one-standard-error rule; report average number of selected variables, MAE/RMSE/rMAE, and multivariate Diebold-Mariano tests against BMT. If a sparse variant (e.g., on average at most 15 variables) is statistically indistinguishable from BMT in accuracy on the same markets, then the parsimony advantage is not unique to BMT and the interpretive conclusion must be revised; if the sparse variants are significantly worse, the current conclusion is supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"To draw the paper's central conclusion, it must be true that BMT's parsimony advantage is not an artifact of the tuning rules used for the competing methods. Section 4 specifies that LASSO and FarmSelect select the regularization parameter via LARS-AIC, Elastic Net via an AIC grid search, while BMT uses the fixed settings p=0.05, c=1, delta1=delta2=1. With d approximately 562, the BMT threshold is roughly Phi^{-1}(1 - 0.05/(2*562)) approximately 3.4, so only very strong signals enter. AIC is known to select many predictors in highly correlated settings like electricity price forecasting; accordingly, Table 4.1 shows LASSO/EN retaining 88-133 variables versus 4.5-8.2 for BMT. The conclusion that 'over-parameterization typically associated with regularization methods is not a necessary price' (Section 5) generalizes from this comparison. But a regularization method tuned by BIC or cross-validation (e.g., the one-standard-error rule) could plausibly select a much smaller model with similar accuracy. The paper provides no such benchmark, so the claim that the over-parameterization is avoidable specifically by BMT, rather than by any sparser tuning, is under-supported. The empirical numbers are not in question; the interpretation is.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":24769,"tokens_out":6799,"duration_ms":60604,"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":[{"comment":"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.'","section":"Section 4.2 and Table 4.1"},{"comment":"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.","section":"Section 4 (implementation settings) and Section 5"},{"comment":"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.","section":"Section 3.3 and Eq. (3.4)"},{"comment":"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.","section":"References and Section 3.3"}],"minor_comments":[{"comment":"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.","section":"Abstract"},{"comment":"In the paragraph on daylight-saving time, the sentence 'Wetransformdaysaffectedbydaylight-savingstotimecontain24observations' is missing spaces between words and should be rewritten as a complete sentence.","section":"Section 2"},{"comment":"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.","section":"Eq. (3.4)"},{"comment":"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.","section":"Section 4.2"},{"comment":"The manuscript does not include a data and code availability statement. Given the practical emphasis on reproducibility and computation time, I recommend adding one.","section":"Data availability"}],"recommendation":"major_revision","confidential_remarks":"The empirical work is solid in design, but the paper's headline claim is too strong and the BMT-versus-AIC comparison needs additional benchmarks. I would also ask the editor to require explicit disclosure of the first author's involvement in the development of BMT, and to request a data and code availability statement, since the full details of the rolling-window implementation are otherwise difficult to verify."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a worthwhile empirical paper, not a breakthrough. The genuinely new piece is BMT applied to electricity price forecasting, and the parsimony result is real. The interpretation, though, is looser than the abstract suggests.\n\nThe paper does several things well. It sets up a clean six-market rolling-window design, uses standard EPF preprocessing (asinh, DST handling), benchmarks against LASSO, Elastic Net, FarmSelect, OCMT, and GOCMT, and runs proper multivariate and univariate DM tests. Reporting is detailed: selection counts, computational times, and heatmaps of variable groups. The finding that BMT matches LASSO/EN accuracy in most markets while retaining roughly 5-8 variables instead of 100-130 is practically useful and not something I had seen before.\n\nThe soft spots are in the claims, not the machinery. The abstract says 'without any loss of forecasting accuracy,' but France is a clear exception: Elastic Net beats BMT at 5% and LASSO at 10% in Section 4.2. That needs qualifying. The stress-test concern also lands: LASSO and EN are tuned by AIC, which is known to select many predictors in correlated settings, while BMT uses a fixed, very stringent threshold (roughly 3.4 with d=562). The parsimony advantage could therefore reflect tuning choices rather than an inherent property of BMT. A BIC or cross-validated LASSO/EN benchmark would settle this. Without it, the conclusion that over-parameterization is 'not a necessary price' is under-supported.\n\nThere is also a theoretical worry the paper does not address: BMT selects the single largest t-statistic at each stage, but the critical values come from OCMT's all-pass rule. The null distribution of a sequential maximum is different, so the stopping rule's validity is an unverified borrowed premise. This may not matter empirically, but it should be flagged. Finally, one of the authors is a co-developer of BMT (Grivas et al. 2026) and the paper does not disclose that overlap when presenting BMT favorably. That is a conflict-of-interest disclosure issue, not a fatal one.\n\nOverall, the empirical work is solid and the paper deserves a serious referee. I would send it to review with a request to fix the abstract, add a sparser-tuning benchmark, and address the disclosure and the theoretical premise. If those are handled, it becomes a useful applied contribution for EPF practitioners.","headline":"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.","tokens_in":25252,"tokens_out":2418,"would_cite":true,"duration_ms":21023,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["electricity price forecasting","variable selection","LASSO","Elastic Net","Boosting with Multiple Testing","multiple testing","model parsimony","Diebold-Mariano test"],"falsifier":"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.","tokens_in":24298,"feed_emoji":"⚡","tokens_out":10221,"duration_ms":79675,"temperature":0.7,"pith_summary":"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.","feed_headline":"BMT matches LASSO forecast accuracy using one-tenth the variables","feed_subtitle":"Four-year rolling forecasts in six European markets show the sparse method matches penalized-regression accuracy.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Introduces BMT and supplies the one-at-a-time selection rule plus simulation evidence that BMT stays parsimonious under multicollinearity.","marker":"Kapetanios et al. (2026)"},{"why":"Presents BMT in generalized linear models and is cited alongside Kapetanios et al. (2026) as a source of the method.","marker":"Grivas et al. (2026)"},{"why":"Introduces OCMT, whose critical value function BMT inherits, and provides the multiple-testing settings used in the comparisons.","marker":"Chudik et al. (2018)"},{"why":"Defines LASSO, the shrinkage benchmark whose forecasting accuracy BMT must match.","marker":"Tibshirani (1996)"},{"why":"Defines Elastic Net, the second shrinkage benchmark in the comparison.","marker":"Zou & Hastie (2005)"},{"why":"Proposes FarmSelect, the factor-adjusted regularization method used as an additional benchmark.","marker":"Fan et al. (2020)"},{"why":"Supplies the equal-predictive-accuracy test used to decide whether BMT's accuracy differs statistically from the baselines.","marker":"Diebold & Mariano (1995)"},{"why":"Provides the 24-equation day-ahead forecasting framework, the area hyperbolic sine preprocessing, and the multivariate Diebold–Mariano implementation used in the study.","marker":"Ziel & Weron (2018)"},{"why":"Documents the variance-stabilizing transformation applied to spot prices before estimation.","marker":"Uniejewski et al. (2018)"},{"why":"Provides the heteroskedasticity-and-autocorrelation-consistent standard errors used in the $t$-statistics at each selection stage.","marker":"Newey & West (1994)"}],"fun_headline_variants":["Sparse BMT matches LASSO accuracy with 10x fewer variables","Electricity forecasting: 10 variables match LASSO's 100","BMT cuts variables by 90%, holds forecast accuracy","One-tenth the predictors, same accuracy: BMT for prices","Parsimony without penalty: BMT ties LASSO in forecasts"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Sparse BMT matches LASSO accuracy with 10x fewer variables","Electricity forecasting: 10 variables match LASSO's 100","BMT cuts variables by 90%, holds forecast accuracy","One-tenth the predictors, same accuracy: BMT for prices","Parsimony without penalty: BMT ties LASSO in forecasts"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000508,"raw_usage":{"total_tokens":2446,"prompt_tokens":890,"completion_tokens":1556,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":506,"completion_tokens_details":{"reasoning_tokens":1467}},"tokens_in":506,"tokens_out":1556,"duration_ms":13552,"temperature":1.0,"reasoning_tokens":1467,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T14:25:12.583407+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":", author Sarafidis, V","cited_arxiv_id":null,"evidence_quote":"Introduces BMT and supplies the one-at-a-time selection rule plus simulation evidence that BMT stays parsimonious under multicollinearity."},{"cited_title":"Nonlinear Boosting with Multiple Testing in High-Dimensional Generalised Linear Models with Binary Responses","cited_arxiv_id":"2607.22440","evidence_quote":"Presents BMT in generalized linear models and is cited alongside Kapetanios et al. (2026) as a source of the method."},{"cited_title":", author Weron, R","cited_arxiv_id":null,"evidence_quote":"Documents the variance-stabilizing transformation applied to spot prices before estimation."}],"review_version":2}